Question

One electron and one proton are accelerated by equal potential. Ratio in their deBroglie wavelength is

• A. 1
• B. \( \frac{m_p}{m_e} \)
• C. \( \frac{m_e}{m_p} \)
• D. \( \frac{m_e}{m_p} \)

Hint:

The deBroglie wavelength ratio depends on the mass ratio when two particles are accelerated with equal potential.

Answer 1

The Correct Option is D

Step 1: Using deBroglie relation.
The deBroglie wavelength \( \lambda \) of a particle is given by \[ \lambda = \frac{h}{\sqrt{2mEK}} \] where \( m \) is the mass and \( EK \) is the kinetic energy.
Step 2: Analyzing the options.
Since the kinetic energy is the same for both, the ratio of wavelengths depends on the masses of the particles. Hence, \[ \frac{\lambda_e}{\lambda_p} = \frac{m_p}{m_e} \]
Step 3: Conclusion.
Therefore, the correct answer is option (D).

Final Answer: \[ \boxed{\frac{m_e}{m_p}} \]