Question

If uncertainty in momentum of electron is three times the uncertainty in position, then uncertainty in velocity of electron would be:

• A. $\frac{1}{4m}\sqrt{\frac{h}{3\pi }}$
• B. $\frac{1}{3m}\sqrt{\frac{h}{\pi }}$
• C. $\frac{1}{3m}\sqrt{\frac{4\pi }{h}}$
• D. $\frac{1}{2m}\sqrt{\frac{3h}{\pi }}$

Answer 1

The correct option is D $\frac{1}{2m}\sqrt{\frac{3h}{\pi }}$

$△p=3△x$

or $\frac{1}{3}m△v=△x$

$\because △p\times △x=\frac{h}{4\pi }$

$\therefore \left(m△v\right)\times \left(\frac{1}{3}m△v\right)=\frac{h}{4\pi }$

$△v^2=\frac{3h}{4\pi m^2}△v=\frac{1}{2m}\sqrt{\frac{3h}{\pi }}$