Question

A particle is travelling 4 times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2 : 1, the mass of the particle is :

• A. 8 times the mass of e⁻
• B. 1/16 times the mass of e⁻
• C. 16 times the mass of e⁻
• D. 1/8 times the mass of e⁻

Hint:

De-Broglie wavelength is inversely proportional to momentum ($p=mv$). If wavelength is larger, momentum must be smaller.

Answer 1

The Correct Option is D

Step 1: $\lambda = \frac{h}{mv}$.
Step 2: $\frac{\lambda_p}{\lambda_e} = \frac{m_e v_e}{m_p v_p}$.
Step 3: $\frac{2}{1} = \frac{m_e}{m_p} \times \frac{v_e}{4v_e} \implies 2 = \frac{m_e}{4m_p} \implies m_p = \frac{m_e}{8}$.