Imagine an atom made up of a stationary proton and a hypothetical particle of double the mass of ele — Atomic Structure Chemistry Question
Question
Imagine an atom made up of a stationary proton and a hypothetical particle of double the mass of electron but having the same charge as the electron. Apply Bohr atomic model and consider all possible transitions of this hypothetical particle directly to the first excited state. The longest wavelength photon that will be emitted has wavelength (given in terms of Rydberg constant $R$ for the hydrogen atom) equal to
💡 Solution & Explanation
Since mass is doubled ($2m_e$), the modified Rydberg constant is $R' = 2R$. The first excited state is $n=2$. Longest wavelength transition directly to $n=2$ is from $n=3$. $\frac{1}{\lambda} = R'\left(\frac{1}{2^2} - \frac{1}{3^2}\right) = 2R\left(\frac{1}{4} - \frac{1}{9}\right) = 2R\left(\frac{5}{36}\right) = \frac{10R}{36} = \frac{5R}{18}$. Thus, $\lambda = \frac{18}{5R}$. Therefore, correct answer is C.