Question

What would be thw minimum uncertainty in de-Broglie wavelenght 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 $0.625\mathring{A}$

${\lambda }_{D.B}=(150/6{)}^{-}1/2A^0=5A^0$

and $\Delta x.\Delta p>=h/4\pi$

and $p=h/\lambda$ or $\Delta p=h\Delta \lambda /{\lambda }^2$

$\Delta x.h/{\lambda }^2\Delta \lambda >=h/4\pi$

$1/\pi \times {10}^{-}9/{\lambda }^2\times \Delta \lambda >1/4\pi$

$\Delta \lambda >=2.5/4\times {10}^{-}10$

$\Delta \lambda >=0.625$ $A^0$