Energy Level

Introduction

John Dalton believed that an atom is the smallest microscopic particle contained in a substance. John Dalton does not study microscopic particles in solids. Instead, he mostly studied the particles of gases. Even though J.J. Thomson explained the neutral nature of atoms, he was unable to explain the concept of the nucleus in the atom. In 1909, Ernest Rutherford introduced a new theory of nuclear power.

Ernest Rutherford, a British physicist, was involved in the study of atoms through radioactive probes using alpha particles. Rutherford’s atomic model is modified by Niels Bohr. The stability of the atom and the line spectrum of the hydrogen atom was modified by Niels Bohr which is explained by Rutherford. He was the first to provide an adequate conceptual explanation of the atomic system to explain the line spectrum of the hydrogen atom.

What are Energy Levels?

The energy levels or orbits or shells of the atom are defined as the constant circular paths, where the electrons in an atom move around the nucleus. If you take an atom, the electrons revolve around the nucleus. However, electrons cannot choose the orbits they surround themselves with. These electrons are orbited by some specific energy. Every orbit consists of different energy levels. Electrons orbit the nucleus in several shells or stable energy levels. Electrons emit energy or accept energy when they jump from one level to another. This energy manifests as a photon.

Fig.1. Energy level of an atom

Quantum Number

The identity of each electron in an atom is based on its four quantum numbers. A quantum number is like a door number.

For example, if we mark any location we wrote the first country, state, city, and street at last we will mention the door number. Similarly, we can denote the location of electrons in an atom. The numbers that represent the arrangement and distribution of atomic orbitals and electrons inside an atom are called quantum numbers.

Bohr Model of an Atom

An electron orbits around the nucleus due to Coulomb’s electrostatic attraction. The centripetal force which is used to keep the movement of electrons in an orbit is provided by this Coulomb force. Electrons in an atom are scattered around the nucleus in separate paths; Electrons do not radiate electromagnetic energy as they move along these paths. Thus the allowed individual orbits are stable. The angular momentum of an electron in such stable orbits is quantized. That means its value is a whole multiple of $\mathrm{\frac{h}{2\pi}}$. It can be written as $\mathrm{l=nħ}$. Here ħ is the short form of Planck’s Constant $\mathrm{\frac{h}{2\pi}}$ and n is the quantum number. This condition is the quantization condition. The electrons and some particles have dual nature. And the circumference of the electron orbit must be the whole multiple of the de Broglie wavelength.

$$\mathrm{2\pi r=n\lambda }$$

Here n=1,2,3,......

From De Broglie Wavelength equation $\mathrm{\lambda =\frac{h}{mv}}$ Here ‘h’ is Planck's constant.

$$\mathrm{\therefore\:2\pi r=n(\frac{h}{mv})}$$

$$\mathrm{mv r=n(\frac{h}{2\pi})}$$

When any particle of mass m and velocity υ moves in a circular motion of radius r, the numerical value of its angular momentum is

$$\mathrm{l=r(mv)}$$

$$\mathrm{mvr=l=n ħ}$$

The energies of orbitals are not constant but have individual values. These individual values are known as the quantization of energy. When an electron absorbs or emits the photon, it jumps to another orbital. During this process, energy is produced. This energy is equal to the energy between two orbitals.

$$\mathrm{\Delta E=E_{final}-E_{initial}=h v=h\frac{c}{\lambda}}$$

c- speed of light; $\mathrm{\lambda}$ - wavelength of the radiation; ν - frequency of the radiation. The energy variation of the atom determines the frequency of the emitted radiation. The frequency of orbital motion does not affect the energy variation.

Bohr’s Explanation of Energy Levels

• The energy levels or orbits or shells of the atom are defined as the constant circular paths, where the electrons in an atom move around the nucleus.

• Electrons do not gain or lose energy in their orbits. Each orbit has a fixed energy level, Bohr called them energy states or energy levels.

• When an electron moves to higher or lower energy levels, it will absorb or emit the energy.

• 1,2,3,4 are the names given to the orbitals which produce the energy. They are also named K, L, M, and N shells. These numbers are called primary quantum numbers (n).

• The K shell closest to the nucleus (n=1) has the lowest energy. The higher energy levels are named respectively L, M, and N. As the distance from the nucleus increases, so does the energy of the orbit.

• The maximum number of electrons that can occupy an energy level (n) is $\mathrm{2n^{2}}$. The energy is absorbed when an electron jumps to a higher energy level from a lower energy level. When an electron jumps to lower energy from a higher energy level, energy is released.

Conclusion

The energy levels or orbits or shells of the atom are defined as the constant circular paths, where the electrons in an atom move around the nucleus. The numbers that represent the arrangement and distribution of atomic orbitals and electrons inside an atom are called quantum numbers. Every orbit consists of different energy levels. The energies of orbitals are not constant but have individual values. The individual values of orbitals are called the quantization of energy. Electrons do not gain or lose energy in their orbits. Each orbit has a fixed energy level, Bohr called them energy states or energy levels.

FAQs

Q1. What is the difference between a hydrogen atom and a deuterium atom?

Ans. The difference between a hydrogen atom and a deuterium atom is that a hydrogen atom does not have neutrons but it consists of both electron and proton whereas a deuterium atom consists of one proton, one neutron, and one electron.

Q2. What is deuterium atom?

Ans. H.C. Urey and his team discovered in 1931 that even (primary) faint lines accompany the hydrogen spectral lines at shorter wavelengths. Isotopes of the same element emit slightly different spectral lines due to the isotope displacement effect (or isotope drift). The appearance of these faint lines confirmed the presence of an isotope in the hydrogen atom. This was named deuterium.

Q3. What is Valence?

Ans. The valence of an element is the degree of ability of that element to combine with another element. And it is equal to the number of electrons participating in the chemical reaction. Elements with valence electrons like 1, 2, 3, 4 have valence 1, 2, 3, 4. If the valence electrons of an element are 5, 6, 7 then its valence is 3, 2, 1. That means 3. 2, 1 electrons are required respectively to get 8 electrons required to achieve atomic stability. If the outer shell of an atom is filled with electrons, the valency of the atom is zero.

Q4. Explain Rutherford’s atomic theory

Ans. Most of the atom is empty. The nucleus is a highly positively charged region at the center of an atom. The size of an atom is very big compared to the nucleus. The circular path taken by the electrons around the nucleus is called an orbit. An atom is generally neutral. That is the number of protons and electrons in an atom is equal. Rutherford’s atomic structure corresponds to that of the solar systems.

Q5. What is Bohr Bury rule?

Ans. Electrons move around the nucleus in circular paths called orbits. The sharing of electrons to fill each of the orbitals is called electron sharing. The shared filling of electrons in these orbitals in atoms takes place subject to certain conditions. These laws are called Bohr and Bury’s rules of electron structure.