Question

The ratio of de Broglie wavelengths of a proton and a deuteron accelerated by potential V_p and V_d respectively, `(lambda_p/lambda_d)` is `1/2`. Find `V_p/V_d`.

Answer 1

de-Broglie wavelength of electrons,

`lambda = h/sqrt(2 m q V)`

∴ `lambda_p = h/sqrt(2 m_pq_pV_p)`

and `lambda_d = h/sqrt(2m_dq_pV_p)`

∴ `lambda_p/lambda_d = 1/sqrt(2m_pq_pV_p) xx sqrt(2m_dq_dV_d)/1`

`lambda_p/lambda_d = sqrt((m_dq_dV_d)/(m_pq_pV_p)`

`lambda_p/lambda_d = sqrt((2m_dq_dV_d)/(m_pq_pV_p))           ...[(because m_d = 2m_p),(and q_d = q_p)]`

`1/2 = sqrt((2V_d)/(V_p)`

`1/4 = (2V_d)/V_p`

`V_p/V_d = 8/1`

V_p : V_d = 8 : 1