CHAPTER 12 ATOMS
What is Atom?
Atoms are tiny particles that comprise all the things in the known universe. Atoms of an element are responsible for all chemical reactions occurring in nature. We know that atoms are made up of three fundamental particles namely,
- Electrons
- Protons
- Neutrons
These particles are also called subatomic particles as they are found inside atoms. An atom is the basic building block of matter and all the thing around us is made up of combing atoms in different proportions. Let’s learn more about Atom, its constituents, and its structure in detail in this article.
Table of Content
Atom Definition
Atoms are defined as the smallest particle that can exist independently in nature and can participate in a chemical reaction. Atoms are the building block of all the matter in the universe. The word term “atom” is derived from the Greek word “Atmos” meaning indivisible. It was viewed that if we break the matter into smaller parts the smallest part so obtained is called the atom. But we know today that atoms can be further divided into fundamental particles.
Structure of Atom
Atoms are the smallest part of an element and between the 18th and 19th centuries, many scientists proposed their theories regarding the structure of atoms based on their studies. These theories were published to elaborate on the structure of atoms, and its constituent.
The most appreciated theories about the atomic model were proposed by,
- John Dalton’s Dalton’s Atomic Theory
- J.J Thomson’s Thomson’s Atomic Model
- Niels Bohr’s Bohr’s Model of an Atom
- Ernest Rutherford’s Rutherford’s Atomic Model
These theories give us an idea about the structure of the atom and the general output of all the theories is that,
“An atom consists of two parts a nucleus which lies at the center and carries a proton (positively charged particle) and neutron (they do not carry any of the charges) and the other part is the outer shell that carries electrons (negatively charged particles). The electrons present in the outer shells continuously revolve around the nucleus without losing any energy.”
The image shown below gives the general structure of the atom.
Learn more about, Structure of Atom
Now let’s learn about these fundamental particles, Electrons, Protons, and Neutrons in detail.
What are Electrons?
Electrons are negatively charged particles that are present in the energy shells of an atom surrounding the nucleus. In the year 1897, J.J Thomson discovered electrons with his cathode ray tube experiment. The charge of an electron is equal and opposite to that of a proton held by the atom. Both charges neutralize each other and hence, atoms are neutral in nature.
Properties of Electrons
The basic property of the electrons are,
- Charge of Electron: An electron is a negatively charged particle. It carries a negative unit.
Charge on an electron = -1.602 × 10-19 Coulombs
- Mass of an electron: The mass of an electron is negligible in an atom. Its mass is 1/1837 of a proton.
Mass of a proton = 9.1093 × 10 -31 Kg
What are Protons?
Protons are the positively charged particles that are present in the nucleus of an atom. In the year 1886 Goldstein found that the charge and mass ratio of these positively charged particles depends on the nature of the gas. This concludes that the charge-to-mass ratio(e/m) is different for different gases.
Properties of Protons
The basic property of the protons are,
- Charge of Proton: Proton is positively charged. The charge of a is equal to the number of charges in an electron(negative charge).
Charge on a proton = +1.602 × 10-19 Coulombs
- Mass of proton: The mass of a proton is considered to be equal to a hydrogen atom. As a hydrogen atom consists of one electron and a proton in which the mass of an electron is negligible therefore it can be said that the mass of a proton is equal to a hydrogen atom.
Mass of a proton = 1.676 × 10 -27 Kg
What are Neutrons?
Neutrons are subatomic particles that are neutral in nature. They do not carry any of the charges. Neutrons are the major constituent of the nucleus and lie along with protons. The mass of a neutron ranges slightly greater than a proton in magnitude. The protons and neutrons present in the nucleus are responsible for the chemical properties of an atom.
The concept of the neutron was proposed by Ernest Rutherford in 1920. And was discovered by the British physicist James Chadwick in 1932.
Properties of Neutrons
The basic property of neutrons are,
- Charge on a neutron: As neutrons are neutrally charged subatomic particles the charge carried by them is 0.
Charge on Neutron = 0
- Mass of a neutron: The mass of a neutron can be calculated by subtracting the mass of the proton from the mass of the deuterium nucleus. The mass of a neutron is 1.008 atomic mass units (amu).
Mass of a neutron = 1.676 × 10-27 Kg
- Although a neutron is a neutral subatomic particle yet it gets affected by the presence of the magnetic field. Due to this its magnetic moment does not equal zero.
- Neutrons are not affected by the electric fields.
History of Atom
According to some scientists, all the atoms in the universe are created 13.7 billion years ago after the Big Bang. Initially, only electrons and quarks are created and millions of years later as the universe cools down quarks aggregated to form protons and neutrons which on further engagement created atoms. These atoms after combining form all the matter in the universe. Early Indian philosophers were the first to think that matter is made up of smaller particles and they call them “Anu” and “Parmanu”. The Greeks were also of the same view. But the modern thinking of atoms was first pioneered by John Dalton.
What is the Size of an Atom?
Atomic Size of an atom is explained in terms of its radius. The distance from the center of the nucleus to the outermost shell of an atom is called its atomic radius. The atoms are very small particles and it is impossible to see atoms through the naked eye. Using a microscope also it is very difficult to see the atom only very powerful electrons microscope are able to see the electrons. The exact size of atoms is not easily calculated, as the location of the electron with respect to the nucleus of the atom can not be found. However can estimate the atomic radius as size to be, 10-9 m.
We can visualize the size of atoms as,
Object | Radii (in m) |
|---|---|
| Atom of Hydrogen | 10-10 m |
| Grain of Sand | 10-4 m |
| A football | 10-1 m |
From the above table, we can observe that a grain of sand has, 106 atoms and a football has 109 atoms.
What is Atomic Mass?
The sum of the number of protons and neutrons is called the atomic mass of the element. The atomic mass as the name suggests is the mass of the atoms. As we know that atoms are made up of electrons, protons, and neutrons and the mass of protons and neutrons is exponentially higher than the mass of electrons so for finding the mass of the atom we find the number of protons and neutrons in the atom.
Atomic Mass is a relative concept and is measured in Atomic Mass Units. We define 1 amu as the 1/12 mass of the carbon (C-12) atom. Hence if we say the mass of a Sodium atom is 23 amu it means it is 23 times heavier than 1/12 of the C-12 atom.
Check, Fractional Atomic Mass
Atomic Mass of Some Common Elements
The atomic masses of some common elements are discussed below in the table:
Elements | Atomic Mass (amu) |
|---|---|
| Hydrogen | 1 |
| Helium | 4 |
| Carbon | 12 |
| Nitrogen | 14 |
| Oxygen | 16 |
| Chlorine | 35.5 |
What is Atomic Number?
The number of protons in an atom is called the Atomic Number of an element. We know that there are various elements and observing all the properties of all the elements individually is tedious work. So we arrange various elements into some group that resembles similar properties. These atoms are arranged on their atomic number. It is the number of protons that any atom has and it is denoted by “Z”.
Atomic Number of Some Common Elements
The atomic numbers of some common elements are discussed below in the table:
| Elements | Atomic Number |
|---|---|
| Hydrogen | 1 |
| Helium | 2 |
| Carbon | 6 |
| Nitrogen | 7 |
| Oxygen | 8 |
| Chlorine | 17 |
Read More,
- Composition of an Atom
- Atomic Number and Mass Number
- Difference between Atoms and Molecules
- How do Atoms Exist?
FAQs on Atom
Who Discovered Atom?
Atom was first used by the famous Greek philosopher Democritus in 400 B.C.
What is an Atomic Radii?
The atomic radii is defined as the distance between the nucleus and the electrons in the outermost shell of an atom.
Why are Atoms Neutral?
As we know that atoms consist of electrons (negatively charged particles), protons (positively charged particles) and neutrons, and it is electrically neutral because it has an equal number of electrons and protons.
What determines the Mass of an Atom?
The mass of the atom is determined by the nucleons of that atom, i.e. the number of protons and neutrons that the nucleus of the atom has. It is also explained using the mass number of the atom.
Why do Atoms Combine?
Atoms combine to form molecules which are more stable in nature than atoms.
What is the Structure of an Atom?
An Atom is composed of Electrons, Protons and neutrons. The nucleus of the atom consists of protons that are positively charged and neutrons that are neutral. The outer region of atom consists of electrons that are negatively charged.
Alpha Particle Scattering and Rutherford’s Nuclear Model of Atom
In today’s universe, the smallest particle of matter is an atom. It is the smallest possible result obtained by dividing the matter without releasing electrically charged particles. It was first proposed by John Dalton in the name of the Atomic Theory. This theory has its own evolution given by different scientists like J.J Thompson, Ernest Rutherford, Niels Bohr and Erwin Schrödinger. Today well will discuss the Rutherford Model of Atom.
Rutherford Model
Ernest Rutherford was working on the emission of α-particles by the atoms to understand the structure of atoms and with respect to the experiment Rutherford was conducting Geiger and Marsden performed some experiments of their own as shown in the figure.
Experimental setup of Geiger-Marsden experiment
They used a beam of 5.5 MeV emitted from a radioactive source (Bismuth) at a thin layer of foil made of gold. α-particles emitted by the source are concentrated into a single beam of light which was allowed to strike the thing gold foil and the concentrated beam is scattered after hitting and can be seen in the screen through a microscope.
This experiment was conducted and the result was that in the scattered beam of light, many particles pass through the foil without collusion, just 0.14% of incident particles scatter more than 1o and 1 in 8000 particles deflect more than 90o. This means that the particle was scattered completely to the backward direction which means there must be some kind of big repulsive force
Why did that 1 in 8000 deflect?
Rutherford said from the observation that the greater repulsive force can be provided if the mass and positive charge is concentrated at the center which will cause the reflection.
So, in Rutherford’s model of the atom, all the positive charge and the mass are at the centre and the electrons will move around it like planets around the sun at some distance.
Rutherford said the size of the atom will be 10-15 approximately but in actual it was 10-10 and as electrons move around at some distance the atom is mostly empty space. Thus, because of such a large empty space in an atom, it is evident that most of the α-particles pass right through the atom and when any α-particles come near the nucleus, they are scattered due to the electric field.
Scattering of the α-particles
As we all know, the gold foil is very thin, so we can assume that the α-particles will not suffer more than one collision. Thus the calculation was needed for a single nucleus. α-particles are nuclei of a helium atom, thus carrying 2 units (2e). The charge of the gold nucleus is Ze where Z is the atomic number of gold.
In this experiment, particles of gold are much heavier than an α-particle, the gold particles won’t move when the scattering occurs. The trajectory can be calculated by using Newton’s second law of motion and coulomb’s law of electrostatic force of repulsion between α-particles and positively charged nucleus which can be written as,
F = 1/(4πε0) × (2e)(Ze)/r2
where,
- r = distance between the α-particles and the nucleus.
- Ze = Charge of the gold nucleus
Alpha-particle trajectory
The trajectory of the alpha particle depends on the impact parameter ( the perpendicular distance of the initial velocity vector of the α-particle from the centre of the nucleus. in the above figure, there are various probabilities for the alpha particles to scatter on, and as you can see the α-particle close to the nucleus is the one that suffers the larger scattering. Now, the α-particle which hits the nucleus direct can face the scattering of even 180 degrees.
But through observation, it is evident that there are not many particles undergoing this 180-degree deviation because the number of particles returned was significant.
Electron orbits in Rutherford’s Nuclear Model
The model involves classical concepts which are,
- It looks atom is an electrically neutral sphere.
- It has a very small, massive and positively charged nucleus at the centre.
- The nucleus at the centre is surrounded by revolving electrons.
- These electrons revolve in their respective orbits around the nucleus.
- The electrostatic force of attraction (Fe) between the revolving electrons and nucleus provides the required centripetal force (Fc) to maintain the rotation of the electrons around the nucleus]
Thus this can be represented as,
Fe – Fc
[1/(4πεo)] × [e2/r2] = mv2/r
thus the relation between the orbit radius and the electron velocity is
r = e2/(4πεomv2)
as we all know, kinetic energy (k) = 1/2 × (mv2)
then kinetic energy becomes,
K = e2/(8πεor)
Similarly, Potential energy (U) becomes,
U = -e2/(4πεo)
therefore total energy becomes the addition of kinetic and potential energy
T = K + U = [e2/(8πεor) + (-e2)/(4πεor))]
T = -e2/(8πεor)
thus, the total energy of electrons is negative which implies that electrons are electrically bonded to the nucleus.
Sample Problems
Problem 1: In Rutherford’s nuclear model of the atom, the nucleus is analogous to the sun which is about which electrons move around the orbit (radius ≅ 10-10 m) like the earth orbits around the sun. If the dimensions of the solar system had the same proportions as those of the atom, would the earth be closer to or farther away from the sun than actually, it is? The radius of the earth’s orbit is about 1.5 × 1011 m. The radius of the sun is taken as 8 × 108
Solution:
The ratio of the radius of electron’s orbit to the radius of nucleus is (10-10m/10-15m) = 105
therefore it is seen that the radius of the electron’s orbit is 105 times larger than radius of nucleus.
If we consider the same situation for the earth and the sun i.e. earth’s orbit around sun were 105 times larger than radius of the sun, then the radius of the earth according this condition will be
105 × 8 × 108m = 8 × 1013 m which is without doubt prolonged than the actual orbit of earth and hence earth would be much farther away from the sun.
It also implies that an atom contains a much greater fraction of empty space as compared to our solar system.
Problem 2: It is experimentally found that 13.6 eV energy is required to separate a hydrogen atom into a proton and electron. Compute the orbital radius and the velocity of the electron in a hydrogen atom.
Solution:
Total energy of electron in hydrogen atom is -13.6 eV = -13.6 × 1.6 × 10-19 J
According to relation between orbit radius and electron velocity we get,
E = -e2/(8πεo r)
E = -2.2 × 10-18 J
Thus the orbital radius becomes,
r = -e2/(8πεo E)
r = [(9 ×109 N m2 /C2) (1.6 × 10-19 C)2 ] / [(2) (-2.2 × 10-18 J)]
r = 5.3 × 10-11 m.
Thus velocity of the electron can be computed by
v = e / (√4 πεomr)
v =2.2 × 106 m/s
Conceptual Questions
Question 1: Which radioactive source was used in the Alpha-particle scattering experiment by Geiger and Marsden?
Answer:
The radioactive element used in the alpha scattering experiment is an radioactive isotope of Bismuth (214 Bi 83).
Question 2: What was the ratio of the deflection in the Alpha-scattering experiment for 90o?
Answer:
1 out of 8000 of the Alpha particles were deflected over 90o .
Question 3: Explain the behaviour of the Alpha particles when they hit the gold foil in the Alpha scattering experiment.
Answer:
When the alpha particles from the source hit the gold foil, many of them pass straight through the gold foil, just about 0.14 % of the particles which collide with the nucleus scatter more than 1o, 1 in 8000 particle deflect more than 90° and Very few of them hit the nucleus head on and returned back to the source’s direction i.e. 180o.
Question 4: Which two laws are used to calculate the trajectory of the collided alpha particle?
Answer:
The Newton’s second law of motion and coulomb’s law of electrostatic force of repulsion between α-particles and positively charged nucleus.
Question 5: State any two properties of an atom given by Rutherford’s Nuclear Model.
Answer:
The properties of an atom given by Rutherford’s Nuclear Model are:
- The nucleus at the center is surrounded by revolving electrons.
- These electrons revolves at their respective orbits around nucleus.
Question 6: Why did the Alpha particles change the trajectory when collided with the nucleus? Why didn’t the Alpha particles?
Answer:
Alpha particles are very lighter then the Gold particles. When two substance have different masses, and the lighter one collided with the heavier one, the lighter one is deflected from its path.
Question 7: Why is the trajectory different for the particles which are collided at different areas of the nucleus?
Answer:
According to the observation from the scattering experiment the nucleus have a repulsive force and it is concentrated at the center. So When the electron is collided head on it is deflected back at 180o and when the particles are collided further above or below the center or even passes close to the nucleus it is deflected to its respective angle.
Atomic Spectra
Atomic Spectra is the spectrum of radiation of electromagnetic waves produced due to the transition of an electron from one energy level to another level within an atom. Atoms have an equal number of negative and positive charges. Atoms were described as spherical clouds of positive charges with embedded electrons in Thomson’s concept. In Rutherford’s model, one tiny nucleus carries the majority of the atom’s mass, as well as its positive charges, and the electrons orbit it.
Every element’s atoms have their own unique spectra and are stable. The spectrum is made up of line spectrums, which are parallel lines that are isolated. In this article, we will learn atomic spectra, its definition, and more in detail.
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Postulates of Bohr Atomic Model
The foundations of quantum mechanics were laid by Niels Bohr, and they are as follows:
- The electrons in the hydrogen atom spin around in stable orbits, generating no radiant energy.
- The angular momentum in stationary orbits is a multiple of the equation h / 2,Ï€ and L = n h / 2Ï€, where n is known as the quantum number.
- The electron changes from a non-radiating orbit to a lower-energy orbit. When this occurs, a photon with the same energy as the difference between the final and beginning states is emitted. hv= Ei Ef is used to calculate frequency (v).
What is Atomic Spectra?
An electron’s spectrum of electromagnetic radiation is released or absorbed as it moves between different energy levels within an atom. When an electron moves from one energy level to the next, it emits or absorbs light of a given wavelength.
The atomic spectra of atoms are the collection of all these unique wavelengths of the atom in a certain set of variables such as pressure, temperature, and so on. Emission spectra, absorption spectra, and continuous spectra are the three forms of atomic spectra.
The Rydberg formula clearly divides the atomic hydrogen emission spectrum into a number of spectral lines with wavelengths. Atomic transitions between different energy levels cause the observable spectral lines in the hydrogen emission spectrum. In astronomical spectroscopy, spectral series are very important.
Atomic Spectroscopy
The study of the electromagnetic radiation received or emitted by atoms is known as atomic spectroscopy. There are three different forms of atomic spectroscopy:
- The transfer of energy from the ground state to an excited state is the subject of atomic emission spectroscopy. Atomic emission can explain the electronic transition.
- Atomic absorption spectroscopy: For absorption to occur, the lower and higher energy levels must have equivalent energy differences. The notion that free electrons created in an atomizer can absorb radiation at a given frequency is used in the atomic absorption spectroscopy principle. The absorption of ground-state atoms in the gaseous state is measured.
- Atomic fluorescence spectroscopy combines atomic emission and atomic absorption since it uses both excitation and de-excitation radiation.
Uses of Atomic Spectroscopy
- It is used to identify the spectral lines of metallurgical materials.
- It is utilised in the pharmaceutical industry to detect traces of materials that have been used.
- It can be used to investigate elements with multiple dimensions.
Spectral Series
A spectral series is a collection of wavelengths arranged in a logical order. Light, or any electromagnetic radiation released by energised atoms, has this property.
Because the hydrogen atom is the most basic atomic system found in nature, it produces the most basic series. When a slit allows a beam of light or other radiation to enter the device, each component of the light or radiation forms an image of the source. When resolved under the spectroscope, these images can be seen.
The photos will be in the shape of parallel lines with consistent spacing positioned next to each other. When moving from a higher to a lower wavelength side, the lines will be farther apart on the higher wavelength side and eventually closed. The shortest wavelength has the fewest separated spectral lines, which is referred to as the series limit.
Line spectrum of the hydrogen atom
A hydrogen atom is made up of several line spectrum series, including:
- Pfund Series
- Brackett Series
- Paschen Series
- Balmer Series
- Lyman Series
Spectral Series Formation
Bohr’s atomic model models and well explains the set of energy levels/states that each atom encloses. Quantum numbers (n=1, 2, 3, 4, 5, 6,…..) are used to name energy states. A photon of energy nh – nl is released when electrons jump from higher energy states (nh) to lower energy ones (nl). Because the energy related to each state is fixed, the difference between them is also fixed, resulting in a transition between similar energy states producing the same energy photon.
The electron transition to a lower energy state divides the spectral series into equivalent series. Within the series, the Greek alphabets are utilised to separate the spectral lines of corresponding energy. Hydrogen has the following spectral series:
- Lyman series (nl=1) The series was discovered by Theodore Lyman between 1906 and 1914. As a result, it bears his name. When electrons transition from higher energy states (nh=2, 3, 4, 5, 6,…) to nl=1 energy states, according to Bohr’s model, the Lyman series appears. The Lyman series’ wavelengths are all in the Ultraviolet band. For a list of wavelengths related to spectral lines, see the table below:
Energy level (n) | Wavelength (in nm) in vacuum |
|---|---|
∞ | 91.175 |
6 | 93.78 |
5 | 94.974 |
4 | 97.256 |
3 | 102.57 |
2 | 121.57 |
- Balmer series (nl=2) Johann Balmer was the first to discover the series in 1885. As a result, the series is named after him. The Balmer series emerges when electrons go from higher energy levels (nh=3,4,5,6,7,…) to a lower energy state (nl=2). The wavelengths of the Balmer series are all visible in the electromagnetic spectrum (400 nm to 740 nm). The H-Alpha line of the Balmer series, which is also a part of the solar spectrum, is used in astronomy to identify hydrogen. See the table below for a list of wavelengths associated with spectral lines.
Energy level (n) | Wavelength (in nm) in air |
|---|---|
∞ | 364.6 |
7 | 397.0 |
6 | 410.2 |
5 | 434.0 |
4 | 486.1 |
3 | 656.3 |
- Paschen series (nl=3) In 1908, a German physicist named Friedrich Paschen was the first to notice the series. As a result, the series is named after him. The Paschen series develops when electrons migrate from higher energy levels (nh=4, 5, 6, 7, 8, …) to lower energy states (nl=3). All of the wavelengths in the Paschen series are in the infrared portion of the electromagnetic spectrum. The Brackett series, which has the smallest wavelength, overlaps with the Paschen series. This series overlaps with all subsequent ones. See the table below for a list of wavelengths associated with spectral lines.
| Energy level (n) | Wavelength (in nm) in air |
|---|---|
∞ | 820.4 |
8 | 954.6 |
7 | 1005 |
6 | 1094 |
5 | 1282 |
4 | 1875 |
- Brackett series (nl=4) In the year 1922, an American physicist named Friedrich Sumner Brackett spotted the series for the first time. As a result, the series is named after him. The Brackett series develops when electrons move from higher energy levels (nh=5, 6, 7, 8, 9 …) to lower energy states (nl=4). The wavelengths of the Brackett series are all in the infrared region of the electromagnetic spectrum. See the table below for a list of wavelengths associated with spectral lines.
Energy level (n) | Wavelength (in nm) in air |
|---|---|
∞ | 1458 |
9 | 1817 |
8 | 1944 |
7 | 2166 |
6 | 2625 |
5 | 4051 |
- Pfund series (nl=5) In 1924, August Harman Pfund became aware of the series for the first time. As a result, the series is named after him. The Pfund series emerges when an electron transitions from a higher energy state (nh=6, 7, 8, 9,10, …) to a lower energy level (nl=5). The wavelengths of the Pfund series are all in the infrared region of the electromagnetic spectrum. See the table below for a list of wavelengths associated with spectral lines.
Energy level (n) | Wavelength (in nm) in vacuum |
|---|---|
∞ | 2279 |
10 | 3039 |
9 | 3297 |
8 | 3741 |
7 | 4654 |
6 | 7460 |
- Humphreys series (nl=6) In 1953, an American physicist called Curtis J Humphreys spotted the series for the first time, and the series is named after him. The Humphreys series develops when electrons migrate from higher energy levels (nh=7, 8, 9, 10, 11…) to a lower energy state (nl=6). The wavelengths of the Humphreys series are all in the infrared region of the electromagnetic spectrum. For a list of wavelengths linked with spectral lines, see the table below.
Energy level (n) | Wavelength (in μm) in vacuum |
|---|---|
∞ | 3.282 |
11 | 4.673 |
10 | 5.129 |
9 | 5.908 |
8 | 7.503 |
7 | 12.37 |
Also, Check
Frequently Asked Questions on Atomic Spectra
1. What are Atomic Spectra?
The spectrum of electromagnetic radiation emitted or absorbed by an electron as it transitions between different energy levels within an atom is known as atomic spectra.
2. In physics and chemistry, What does the term “Spectrum” Mean?
The meaning of spectrum is the same in physics as it is in chemistry. When white light is allowed to flow through a prism, it produces a band of colours on a screen.
3. What do Atoms consist of?
Atoms have an equal number of negative and positive charges. Atoms were described as a spherical cloud of positive charges with embedded electrons in Thomson’s concept.
4. What Is the Number of Spectral Lines?
When electrons shift from higher energy levels to lower energy levels, spectral lines appear. The following are the two types of spectral lines:
- Emission lines: Emission lines are a type of spectral line that can appear in a variety of colours and have a black background. Only when the particles emit the wavelength can these lines be seen.
- Absorption lines are a type of spectral line that can be classified in two ways. These could take the form of dark coloured bands on a black background. When the particles absorb the wavelengths, these lines appear.
5. In the spectrum, How many Spectral Lines may be seen?
When moving from higher to lower energy levels, the spiritual lines can be seen. The concept of numerous spectral lines has been generalised after several research. The elements of the fourth energy level migrate to the third level, and then two second-level elements move to the first level.
6. Mention different series of the spectrum and where the lines fall on the spectrum.
The many series of the spectrum, as well as the various sections of the spectrum where the lines lie, are shown below:
- The UV band is part of the Lyman Series.
- H alpha line from the Balmer series
- Infrared region of the Paschen Series
- The Brackett Series is an electromagnetic spectrum that exists in the infrared area.
- Infrared region Pfund series
- Infrared region of the Humphreys series.
Bohr’s Model of the Hydrogen Atom
The Bohr model of the hydrogen atom was the first atomic model to successfully explain the atomic hydrogen radiation spectra. Niels Bohr proposed the atomic Hydrogen model in 1913. The Bohr Model of the Hydrogen Atom attempts to fill in some of the gaps left by Rutherford’s model. It has a special place in history because it introduced the quantum theory, which gave rise to quantum mechanics.
In comparison to the valence shell atom model, the Bohr model is a more rudimentary representation of the hydrogen atom. It may be determined as a first-order approximation of the hydrogen atom using the broader and far more precise quantum mechanics, and hence may be regarded as an obsolete scientific theory. Arthur Erich Haas suggested an analogous quantum model in 1910, but it was rejected until the 1911 Solvay Congress. The old quantum theory refers to the quantum theory that existed between Planck’s discovery of the quantum (1900) and the introduction of mature quantum mechanics (1925).
Planetary Model of the Atom
Quantum mechanics first appeared in the mid-1920s. One of the founders of quantum mechanics, Neil Bohr, was interested in a hotly debated topic at the time – the structure of the atom. Numerous atomic models had emerged, including J.J. Thompson’s theory and Ernest Rutherford’s discovery of the nucleus. However, Bohr supported the planetary model, which stated that electrons revolved around a positively charged nucleus in the same way that planets revolved around the sun.
Bohr model of hydrogen atom postulates
- An atom, such as a hydrogen atom, has numerous stable circular orbitals in which an electron can remain.
- An electron remains in a specific orbit in which no energy is emitted or absorbed.
- When an electron may jump from one orbit to another with more energy absorption but from one orbit to another with lower energy emission.
- An electron’s angular momentum in an orbit is an integral multiple of h/2Ï€. This integral multiple is known as the hydrogen atom’s primary quantum energy level. As a result, mvr = nh/2Ï€, where m = electron mass, v = electron tangential velocity, and r = radius of Bohr energy levels.
Atomic line spectra
Another example of quantization is atomic line spectra. When an element or ion is heated by a flame or excited by an electric current, the excited atoms emit light of a specific color. The emitted light can be refracted by a prism, resulting in spectra with a distinct striped appearance due to the emission of specific wavelengths of light. The wavelengths of some emission lines could even be fitted to mathematical equations in the relatively simple case of the hydrogen atom. The equations, however, did not explain why the hydrogen atom emitted those specific wavelengths of light. Prior to Bohr’s model of the hydrogen atom, scientists were baffled as to why atomic emission spectra were quantized.
Bohr’s Equation
The Bohr Model of the Hydrogen Atom proposed the planetary model first, but an assumption about electrons was later made. The assumption was that the structure of atoms could be quantized. Bohr proposed that electrons orbited the nucleus in fixed-radius orbits or shells. Only shells with the radius specified by the equation below were permitted, and electrons could not exist between these shells. The equation gives the mathematical expression for the allowed value of the atomic radius.
r(n) = n2 × r(1)
Where n is a positive integer and r(1) is the smallest radius allowed for the hydrogen atom, also known as the Bohr’s radius. The radius of Bohr has the value:
r(1) = 0.529 × 10-10 m
By considering electrons in circular, quantized orbits, Bohr calculated the energy of an electron in the nth level of hydrogen as:
E(n) = -(1/n2) × 13.6 eV
Where E is the lowest possible energy of a hydrogen electron and 13.6 eV is the lowest possible energy of a hydrogen electron E(1). The obtained energy is always a negative number, with the ground state n = 1 having the most negative value. The reason for this is that the energy of an electron in orbit is relative to the energy of an electron completely separated from its nucleus, n=infinity, which has an energy of 0 eV. Because an electron in a fixed orbit around the nucleus is more stable than an electron far from its nucleus, the energy of the electron in orbit is always negative.
Absorption and Emission: To be excited to a higher energy level, an electron would absorb energy in the form of photons, according to Bohr’s model. The excited electron is less stable after escaping to a higher energy level, also known as the excited state, and would therefore rapidly emit a photon to return to a lower, more stable energy level. The energy difference between the two energy levels for a specific transition is equal to the energy of the emitted photon.
Limitations of the Bohr Model of the Hydrogen Atom:
- It violates the Heisenberg Uncertainty Principle by treating electrons as having a known radius and orbit.
- The Bohr Model calculates the ground state orbital angular momentum incorrectly.
- It predicts the spectra of bigger atoms incorrectly.
- The relative intensities of spectral lines are not predicted.
- Fine and hyperfine structures in spectral lines are not explained by the Bohr Model.
- It does not account for the Zeeman Effect.
Although the modern quantum mechanical model and the Bohr Model of the Hydrogen Atom appear to be diametrically opposed, the fundamental idea in both is the same. Classical physics cannot adequately describe all of the phenomena that occur at the atomic level.
Bohr Model for Heavier Atoms
The nucleus of heavier atoms contains more protons than the nucleus of a hydrogen atom. To cancel out the positive charge of all of these protons, more electrons were necessary. Each electron orbit, according to Bohr, could only hold a certain amount of electrons. When the level was full, extra electrons were moved to the next level. Thus, for heavier atoms, the Bohr model explained electron shells. Some of the atomic features of heavier atoms were explained by the model, which had never been replicated before.
For example, the shell model explained why atoms became smaller as they moved through a period (row) of the periodic table while having more protons and electrons. It also explained why noble gases were inert, as well as why atoms on the left side of the periodic table attract electrons while those on the right lose them. However, because the model assumed that electrons in the shells did not interact with one another, it was unable to explain why electrons appeared to stack in an irregular fashion.
Improvements to the Bohr Model
The Sommerfeld model, sometimes known as the Bohr-Sommerfeld model, was the most notable improvement to the Bohr model. Electrons in this scenario travel in elliptical orbits around the nucleus rather than circular orbits. The Sommerfeld model explained atomic spectral effects better, such as the Stark effect in spectral line splitting. The model, however, was unable to handle the magnetic quantum number. In 1925, the Bohr model and models based on it were supplanted by Wolfgang Pauli’s quantum mechanics-based model. That model was modified to produce the present model, which Erwin Schrodinger introduced in 1926. Today, wave mechanics is used to describing atomic orbitals in order to understand the behavior of the hydrogen atom.
Discovery since Bohr’s hydrogen model
The Bohr model did an excellent job of explaining the hydrogen atom and other single-electron systems like He+. Unfortunately, when applied to the spectra of more complex atoms, it did not perform as well. Furthermore, the Bohr model provided no explanation for why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field.
In the decades that followed, scientists such as Erwin Schrödinger demonstrated that electrons can be thought of as both waves and particles. This means that it is impossible to know both an electron’s position in space and its velocity at the same time, as stated more precisely in Heisenberg’s uncertainty principle. Bohr’s idea of electrons existing in specific orbits with known velocity and radius is contradicted by the uncertainty principle. Instead, we can only calculate the chances of finding electrons in a specific region of space surrounding the nucleus.
The modern quantum mechanical model may appear to be a significant departure from the Bohr model, but the central idea remains the same: classical physics is insufficient to explain all phenomena at the atomic level. Bohr was the first to recognize this by incorporating the concept of quantization into the electronic structure of the hydrogen atom, allowing him to explain the emission spectra of hydrogen and other one-electron systems.
Sample Questions
Question 1: What are subatomic particles?
Answer:
Subatomic particles are the particles that make up an atom. Protons, electrons, and neutrons are all included in this category.
Question 2: What are the shortcomings of Bohr’s atomic model?
Answer:
The structure of an atom, according to this atomic model, provides poor spectral predictions for larger atoms. It also failed to account for the Zeeman effect. It could only explain the hydrogen spectrum successfully.
Question 3: How can the total number of neutrons in the nucleus of a given isotope be determined?
Answer:
The total number of protons and neutrons in an isotope is used to calculate its mass number. The total number of protons in the nucleus is described by the atomic number. As a result, the number of neutrons is calculated by subtracting the atomic number from the mass number.
Question 4: How do the atomic structures of isotopes vary?
Answer:
They differ in terms of the total number of neutrons present in the atom’s nucleus, as described by their nucleon numbers.
Question 5: What is the structure of an atom?
Answer:
Atoms are made up of protons, electrons, and neutrons. The protons (positively charged) and neutrons are found in the nucleus (centre) of an atom (without charge). The outermost regions of the atom are known as electron shells, and they contain (negatively charged) electrons.
Spectrum of the Hydrogen Atom
Electrons in a hydrogen atom circle around a nucleus. Because of the electromagnetic force between the proton and electron, electrons go through numerous quantum states. Neil Bohr’s model helps in visualizing these quantum states as electrons orbit the nucleus in different directions.
When Electrons in an atom are supplied energy, they get excited and jump from a lower energy level to a higher energy level. As we know electrons always try to remain in their lowest energy level, the excited electrons go back to their original level and emit radiation in this process. This phenomenon explains the emission spectrum via hydrogen, sometimes known as a hydrogen emission spectrum.
We will go over an experiment to better understand what the Hydrogen emission spectrum is. Consider a thin tube carrying low-pressure gaseous hydrogen. The electrodes will then be attached to both ends of the container. Now, if we apply a high voltage to the electrode, we can see a pink glow (bright) in the tube. We know that a prism divides the light that passes through it by diffraction. The visible light spectrum is a subset of the hydrogen emission spectrum. Because the light is UV, our eyes are unable to perceive the majority of it. The electron transitioning from a high energy state to a low energy state is the primary cause of the hydrogen line emission spectrum.
What is the Spectral emission?
When an electron transitions, or jumps, from a higher energy state to a lower energy one, spectral emission occurs. To distinguish between the two states, the lower energy level is denoted by n1, while the higher energy state is denoted by n2. The energy difference between the two states corresponds to the energy difference of a photon emitted. Because the energy of each state is fixed, so is the energy difference between them, and the transition will always generate the same energy photon.
Electron transitions and their resulting wavelengths for hydrogen.
The quantized energy levels of the atoms lead the spectrum to have wavelengths that represent the differences in these energy levels.
Spectral series of Hydrogen
Because the hydrogen atom is the simplest atomic system known in nature, it forms the simplest of this series. When a light or radiation beam enters the device through a slit, each individual component of the light or radiation forms an image of the source. When resolved with a spectroscope, these images can be seen. The images obtained will be in the shape of parallel lines grouped adjacent to each other with uniform spacing. When moving from the higher to lower wavelength side, the lines will be farther apart on the higher wavelength side and gradually closed on the lower wavelength side. The series limit is the shortest wavelength with the fewest separated spectral lines.
In 1885, the first such series was observed by a Swedish school teacher Johann Jakob Balmer (1825–1898) in the visible region of the hydrogen spectrum. The Balmer series is the part of the hydrogen emission spectrum that is responsible for exciting an electron from the second shell to any other shell. Other such series are mentioned below:
- Lyman series: Electron moves to the first shell from any other shell.
- Balmer series: Electron moves to the second shell from any other shell.
- Paschen series: Electron moves to the third shell from any other shell.
- Bracket series: Electron moves to the fourth shell from any other shell.
- Pfund series: Electron moves to the fifth shell from any other shell.
Rydberg’s formula
The energy differences between levels in the Bohr model, and hence the wavelengths of emitted or absorbed photons, is given by the Rydberg formula:
where,
- Z is the atomic number,
- n1 is the principal quantum number of the lower energy level,
- n2 is the principal quantum number of the upper energy level, and
- R is the Rydberg constant. (1.09677×107 m−1 for hydrogen and 1.09737×107 m−1 for heavy metals).
The wavelength will always be positive because n1 is defined as the lower level and so is less than n2. This equation is valid for all hydrogen-like species, i.e. atoms having only a single electron, and the particular case of hydrogen spectral lines is given by Z=1.
Sample Problems
Problem 1: In a hydrogen atom, an electron undergoes a transition from the second state to the first excited state and then to the ground state. Identify the spectral series to which these transitions belong.
Solution:
Since the atom’s transition is to the first shell, it falls under the category of Layman’s series.
Problem 2: Find the ratio of wavelengths of the last line of the Balmer series and the last line of the Lyman series.
Solution:
We know that,
1/λ=Z2R[1/n12−1/n22]
For the last Balmer series
n1 = 2, n2 = ∞ , Z = 1
1/λb=R[1/22−1/∞2]
λb = 4/R
Similarly, For the last Lyman series
1/λl = R[1/12−1/∞2]
λ1 = 1/R
λb/λl = (4/R)/(1/R)
λb/λl = 4
The ratio of wavelengths of the last line of the Balmer series and the last line of the Lyman series is 4.
Problem 3: The Balmer series in the hydrogen spectrum corresponds to the transition from n1 = 2 to n2 = 3,4,… This series lies in the visible region. Calculate the wavenumber of the line associated with the transition in the Balmer series when the electron moves to n = 4 orbit.
Solution:
We know that
1/λ = Z2R(1/n12-1/n22)
Given,
n1 = 2
n2 = 4
There, the wavenumber is given as,
ν = 1/λ
ν = 109677( 1/4-1/16)
ν = 20564.44 cm-1
Problem 4: When an electron in a hydrogen atom jumps from the third excited state to the ground state, how would the de Broglie wavelength associate with the electron change?
Solution:
Given: For 3rd excited state n2 = 4,
For Ground state, n1 = 1 and Z = 1.
We know that 1/λ = Z2R(1/n12-1/n22)
1/λ = R(1/12-1/42)
1/λ = 109677 × (15/16)
λ = 16/(109677 × 15)
λ = 97 nm, which lies in the UV region
Problem 5: Calculate the shortest wavelength of light emitted in the Paschen series of the hydrogen spectrum. Which part of the electromagnetic spectrum, does it belong to? (Given : Rydberg constant, R = 107 m-1)
Solution:
In the Balmer series, an electron jumps from higher orbits to the third stationary orbit (n1 = 3).
We know that 1/λ = Z2R(1/n12-1/n22), Z=1
1/λ = R(1/32-1/n22)
For the shortest wavelength, n2 should be ∞.
1/λ = R(1/32-1/∞2)
1/λ = 107(1/9)
λ = 9 x 10-7 m
Problem 6: Calculate the shortest wavelength of photons emitted in the Bracket series of the hydrogen spectrum. Which part of the spectrum, does it belong to? [Given Rydberg constant, R = 1.1 × 107 m-1]
Solution:
In bracket series, n1 = 4,
for shortest wavelength , n2 = ∞
We know that 1/λ = Z2R(1/n12-1/n22), Z=1
1/λ = R(1/42-1/∞2)
1/λ = R/16
λ = 16/1.1 × 107
After solving we get λ = 1454 nm, which lies in the Infrared region of the spectrum.
Problem 7: The short wavelength limit for the Lyman series of the hydrogen spectrum is 913.4 A. Calculate the short wavelength limit for the Balmer series of the hydrogen spectrum.
Solution:
λl for layman series = 913.4 Å
We know that 1/λ = Z2R(1/n12-1/n22), Z=1
For the short wavelength of the Lyman series,
1/913.4 = R[1/12−1/∞2]
or
R=(1/913.4)
For a short limit of wavelength for the Balmer series,
1/λb = R[1/22−1/∞2]λb
=4/R
=4(913.4)
or
λb = 365.36 nm.
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