Question

A proton and an electron are associated with the same de-Broglie wavelength. The ratio of their kinetic energies is:
Given: \(h = 6.63 \times 10^{-34} \, \text{Js}\), \(m_e = 9.0 \times 10^{-31} \, \text{kg}\), and \(m_p = 1836 \times m_e\)

• A. \(1 : 1836\)
• B. \(1 : \frac{1}{1836}\)
• C. \(1 : \frac{1}{\sqrt{1836}}\)
• D. \(1 : \sqrt{1836}\)

Answer 1

The Correct Option is A

For the same de-Broglie wavelength, \(P = \frac{h}{\lambda}\) is the same for both the proton and the electron. Kinetic energy is given by:
\[ \text{KE} = \frac{P^2}{2m}. \]
Thus:
\[ \frac{\text{KE}_e}{\text{KE}_p} = \frac{m_p}{m_e}. \]
Given:
\[ m_p = 1836 m_e. \]
Substitute:
\[ \frac{\text{KE}_e}{\text{KE}_p} = \frac{1}{1836}. \]
Final Answer: \(1 : 1836\).