Question

The ratio of de Broglie wavelength of an electron to that of a proton moving with the same kinetic energy is:

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

Hint:

Remember: \[ \lambda \propto \frac{1}{\sqrt{m}} \] Lighter particle has greater de Broglie wavelength.

Answer 1

The Correct Option is A

Step 1: Recall de Broglie wavelength formula. \[ \lambda=\frac{h}{\sqrt{2mK}} \] where: \[ m=\text{mass}, \qquad K=\text{kinetic energy} \]

Step 2: Compare electron and proton wavelengths. For same kinetic energy: \[ \lambda \propto \frac{1}{\sqrt{m}} \] Thus: \[ \frac{\lambda_e}{\lambda_p} = \sqrt{\frac{m_p}{m_e}} \] Therefore: \[ \boxed{\sqrt{\frac{m_p}{m_e}}} \]