Question

Imagine an atom made of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength [Rydberg Constant = R] equal to

• A. $\frac{9}{5R}$
• B. $\frac{36}{5R}$
• C. $\frac{18}{5R}$
• D. $\frac{4}{R}$

Answer 1

The correct option is C $\frac{18}{5R}$

Hence the mass of electron is doubled, energy of the electron will also be doubled.
Therefore, $E_n=-\frac{27.2}{n^2}eV$
Given, transition is being done into first excited state with emission of photon of longest possible wavelength, which is from $n=3$ to $n=2$.
As mass is doubled:

$\frac{1}{\lambda }=2R{Z}^2(\frac{1}{{n_1}^2}-\frac{1}{{n_2}^2})$

$\frac{1}{\lambda }2R(\frac{1}{4}-\frac{1}{9})=\frac{5R}{18}$

Therefore, $\lambda =\frac{18}{5R}$