Question

A moving electron has $2.8\times {10}^{-25}J$ of kinetic energy. Its wavelength is:
(Mass of electron $=9.1\times {10}^{-31}kg$).

• A. $9.2455\times {10}^{-7}m$.
  
• B. $9.2455\times {10}^{-8}m$.
  
• C. $9.2455\times {10}^{-7}cm$.
  
• D. $4.6227\times {10}^{-7}m$.
  

Answer 1

Answer: (A)

$9.2455\times {10}^{-7}m$.

Let $KE$ denote $Kinetic$ $energy$,

$KE=\frac{1}{2}m{v}^2$

$\therefore v=\sqrt{\frac{2KE}{m}}⟹mv=\sqrt{2mKE}$

Now, $\lambda =\frac{h}{mv}$ $\dots$[De-broglie wavelength]

$\lambda =\frac{h}{\sqrt{2mKE}}=\frac{6.6\times {10}^{-23}}{\sqrt{2\times 9.1\times {10}^{-31}\times 2.8\times {10}^{-23}}}=9.2455\times {10}^{-7}m$