Question

If the momentum of an electron is changed by $p_m$, then the de Broglie wavelength associated with it increased by $0.5\%$. The initial momentum of electron will be

• A. $p_m/200$
• B. $p_m/100$
• C. $201p_m$
• D. $100p_m$

Answer 1

The correct option is C $201p_m$

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

${\lambda }_i=\frac{h}{p_i}$

Now

${\lambda }_i+\frac{0.5}{100}{\lambda }_i=\frac{h}{p-p_m}$

$\frac{201}{200}\left(\frac{h}{p}\right)=\frac{h}{p-p_m}$

$201p-201p_m=200p$
$p=201p_m$
So, the answer is option (C).