Question

What would be the minimum uncertainty in de-Broglie wavelength of a moving electron accelerated by potential difference of 6 volt and whose uncertainty in position is $\frac{7}{22}nm$?

• A. $6.25\mathring{A}$
• B. $6\mathring{A}$
• C. $0.625\mathring{A}$
• D. $0.3125\mathring{A}$

Answer 1

The correct option is C $0.625\mathring{A}$

${\lambda }_{D,B}=\sqrt{\frac{150}{6}}\mathring{A}=5\mathring{A}$
and $△x.△p\ge \frac{h}{4\pi };p=\frac{h}{\lambda }or△p=\frac{h}{{\lambda }^2}△\lambda$
$\Rightarrow \frac{1}{\pi }\times \frac{{10}^{-9}}{{\lambda }^2}\times △\lambda >\frac{1}{4\pi }\Rightarrow △\lambda \ge \frac{2.5}{4}\times {10}^{-10}$
$△\lambda \ge 0.625\mathring{A}$