Question

Neglecting variation of mass with energy the wavelength associated with an electron having a kinetic energy E is proportional to

• A. $\sqrt{E}$
• B. E
• C. $E^{-1/2}$
• D. $E^{-2}$

Answer 1

The correct option is C $E^{-1/2}$

Wavelength associated with the electron $\lambda =\frac{h}{p}$
where $h$ is Planck's constant and $p$ is the momentum of electron.
Momentum of electron $p=\sqrt{2mE}$
where $E$ is the kinetic energy of electron.
$⟹\lambda =\frac{h}{\sqrt{2mE}}$
$⟹\lambda \propto E^{-1/2}$
Thus option C is correct.