Atomic StructureHard

Question

The energy of an electron in an orbit of the Bohr's atom is $- 0.04E_{0}eV$ where $E_{0}$ is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck's constant, then $\frac{2\pi\text{ }L}{\text{ }h}$ is $\_\_\_\_$ :

Options

A.2
B.4
C.5
D.6

Solution

Angular momentum $L = \frac{nh}{2\pi}$

$$n = \frac{2\pi\text{ }L}{\text{ }h} $$Energy $E = - \frac{13.6}{n^{2}}.z^{2}$

$$\begin{matrix} & E \Rightarrow - \frac{E_{0}}{n^{2}} = - 0.04E_{0} \\ & n^{2} = 25,n = 5 \end{matrix}$$

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