Question

Imagine an atom made up of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr atomic model and consider all possible transitions of this hypothetical particle to the first excited level. The largest wavelength photon that will be emitted has wavelength $\lambda$ (given in terms of the Rydberg constant $R$ for the hydrogen atom) is 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 $\frac{18}{5R}$

Energy is related to mass: $E_n\propto m$

The largest wavelength ${\lambda }_{max}$ photon will correspond to the transition of particle from $n=3$ to first excited state, $n=2$.

$\frac{1}{{\lambda }_{max}}=2R(\frac{1}{2^2}-\frac{1}{3^2})$

$\frac{1}{{\lambda }_{max}}=\frac{5R}{18}\therefore {\lambda }_{min}=\frac{18}{5R}$

Hence, option C is correct.