Question

If a proton and an electron have the same de Broglie wavelength, the ratio of the velocity of proton to the velocity of electron will be nearly

• A. $1$
• B. $1840$
• C. $\frac{1}{1840}$
• D. $44$

Answer 1

The correct option is C $\frac{1}{1840}$

De Broglie wavelength is given by:

$\lambda =\frac{h}{p}$

If two bodies (electron and proton) have the same De Broglie wavelength, they have the same momentum.
i.e.
$p_1=p_2$
$m_e{v}_e=m_p{v}_p$
i.e.

$\frac{m_e}{m_p}=\frac{v_p}{v_e}=\frac{1}{1840}$

So, the answer is option (C).