A proton and an electron are accelerated by same potential difference have de-Broglie wavelength λp and λe

Q: A proton and an electron are accelerated by same potential difference have de-Broglie wavelength λ_p and λ_e

(A) λ_e = λ_p

(B) λ_e < λ_p

(D) none of these

Solution :

As Proton & electron have same charge and accelerated by same Potential difference V . Therefore Kinetic Energy K = q V will be constant .

De-broglie Wavelength $\large \lambda = \frac{h}{p} = \frac{h}{\sqrt{2 m K}}$

$\large \lambda \propto \frac{1}{\sqrt{m}}$

$\large \frac{\lambda_p}{\lambda_e} = \sqrt{\frac{m_e}{m_p} }$

$\large \frac{\lambda_p}{\lambda_e} < 1 $ (Since m_p > m_e)

Hence , λ_e > λ_p

Correct option is (C)