Question

When the kinetic energy of an electron is increased the wavelength of the associated wave will:

• A. increase
• B. decrease
• C. be none of the above
• D. remain independent upon kinetic energy

Answer 1

Answer: (B)

From de-Broglie equation $\lambda =\frac{h}{p}$

where $h$ and $p$ are the Planck's constant and momentum of the electron respectively.

Kinetic energy of the electron $E=\frac{p^2}{2m}$

$⟹$ $p=\sqrt{2mE}$

$\therefore$ $\lambda =\frac{h}{\sqrt{2mE}}$ $⟹\lambda =\frac{1}{\sqrt{E}}$

Thus wavelength associated with the wave will decrease with the increase in kinetic energy of electron.