A proton when accelerated through a potential difference of V volt has a wavelength `lamda` associated with it. An alpha-particle in order to have the same `lamda` must be accelerated through a potential difference of

Options

A. V volt
B. 4V vold
C. 2 V volt
D. `((V)/(8))` volt

Answer

D

Explanation

`lamda_P=lamda_alpha`
or `(h)/(sqrt(2m_pQ_pV))=(h)/(sqrt(2m_alphaQ_alphaV_alpha))`
`m__pQ_pV_p=m_alphaQ_alphaV_alpha`
`V_alpha=((m_p)/(m_alpha))((Q_p)/(Q_alpha))V=((1)/(4))((1)/(2))V=(V)/(8)`