Question

If the momentum of an electron is changed by P, then the de-Broglie wavelength associated with it changes by 0.5%. The initial momentum of an electron will be:

• A. $400P$
• B. $\frac{P}{200}$
• C. $100P$
• D. $200P$

Answer 1

The correct option is D $200P$

According to de-Broglie relation:

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

let initial momentum $=p_1$ and associated wavelength is ${\lambda }_1$

and with a decrease in wavelength momentum will increase

thus $\Delta p=-P$ for $\Delta \lambda =\frac{0.5}{100}\times {\lambda }_1$

diffrentiating the debroglie relation we get:

$\frac{\Delta \lambda }{{\lambda }_1}=-\frac{\Delta p}{p_1}$

and $\frac{0.005\times {\lambda }_1}{{\lambda }_1}=\frac{P}{p_1}=\frac{0.5}{100}$

$p_1=200P$

option D is correct