Question

The moving particle is associated with wavelength $5\times {10}^{-8}m$. If its momentum is reduced to half of its value, compute the new wavelength.

• A. ${10}^{-7}m$
• B. ${10}^{-8}m$
• C. $2.5\times {10}^{-8}m$
• D. $2\times {10}^{-7}m$

Answer 1

The correct option is A ${10}^{-7}m$

Given $\lambda =5\times {10}^{-8}m$
$\lambda =\frac{h}{mu}=\frac{h}{momentum}$
$\therefore \frac{{\lambda }_1}{{\lambda }_2}=\frac{(momentum{)}_2}{(momentum{)}_1}$
Since, $(momentum{)}_2=\frac{1}{2}(momentum{)}_1$
or ${\lambda }_2=\frac{(momentum{)}_1}{(momentum{)}_2}\times {\lambda }_1=2\times 5\times {10}^{-8}$
$={10}^{-7}m$