Question

If the velocity of a particle is increased three times, then the percentage decrease in its de Broglie wavelength will be :

• A. $33.3$%
• B. $66.6$%
• C. $99.9$%
• D. $22.2$%

Answer 1

The correct option is B $66.6$%

Wavelength, $\lambda =\frac{h}{mv}$

${\lambda }^{{}^{\prime }}=\frac{h}{3mv}$

$\frac{{\lambda }^{{}^{\prime }}}{\lambda }=\frac{1}{3}$

${\lambda }^{{}^{\prime }}=\frac{\lambda }{3}$

$\Delta \lambda =\lambda -\frac{\lambda }{3}$

$=\frac{2\lambda }{3}$

$=66.6$% decrease in$\lambda$

So, the answer is option (B).