Question

If the value of $E = - 78.4{\text{ }}kcal/mole$ , the order of the orbit in a hydrogen atom is:
A.4
B.3
C.2
D.1

Answer 1

In the Bohr model of an atom, the electrons travel in the circular orbits around the nucleus that are defined. These orbits are labeled as the quantum number n. The electrons jump from one orbit to another by emitting energy. There is either absorption or a release of energy.

Formula used: ${E_n} = - \dfrac{{13.6}}{{{n^2}}}eV$

Complete step by step answer:

The formula for calculating the energy of the electron is –
${E_n} = - \dfrac{{13.6}}{{{n^2}}}eV$ where, ${E_n} =$ the energy of the electron, ${n^2} =$ orbits in which the electrons travel or order of the orbit.
The energy of an electron in the first Bohr orbit of H atom = $- 13.6eV$ = $2.61 \times {10^{22}}kcal/mol$ .
To find: order of the energy state for the electron
The formula to calculate the order of an electron is

$$\- \dfrac{{78.6 \times 2.61 \times {{10}^{22}}}}{{6.023 \times {{10}^{23}}}} = - \dfrac{{13.6}}{{{n^2}}} \\\ {n^2} = \dfrac{{6.023 \times {{10}^{23}} \times 13.6}}{{78.6 \times 2.61 \times {{10}^{22}}{\text{ }}}} \\\ {n^2} = 3.99 \\\ n = \sqrt 4 \\\ n = 2 \\\$$

Hence, the correct option is (C)

Additional information:

When a transition of an electron takes place, a corresponding energy line can be measured using Balmer’s method. The collection of such lines for the various energy transformations is known as Balmer’s series. The wavelength of these energy transformations can be calculated by the following formula:
$\dfrac{1}{\lambda } = R(\dfrac{1}{{n_1^2}} - \dfrac{1}{{n_2^2}})$
Where $\lambda$ is the wavelength of the energy, R is the Rydberg constant, ${n_1}$ is the orbit number of the electron from where it is moving, ${n_2}$ is the orbit number of the electron to where it is moving. This formula is also known as Rydberg’s Formula.

Note: A student can get confused between the ground state and the excited state of an electron.
Ground state – The ground state of an electron is the energy level of the electron that it usually occupies. The ground state is the lowest energy state of the electron.
Excited-state – The excited state of an electron is the energy state which the electron temporarily acquires. This state is greater than the ground state.