Question

An electron as de Broglie wavelength 2.0×10^-12m.find the kinetic energy also find the phase and group velocity of its de Broglie waves.

Answer 1

Step by Step explanation:

Given: Wavelength (∧) is $2.0x10^{-12}m$

To find: The Kinetic Energy (k.e.), and Group Velocity (v).

We have ∧$= 2 x 10^{-12}m$

⇒ ∧ $= \frac{h}{mv}$

⇒ $2x10^{-12}m= \frac{6.6x10^{-39}}{9.1x10^{-39}xv}$

i. For calculation of Group Velocity or 'v',

⇒ $v=$ $\frac{6.6x10^{-34}}{9.1x10^{-39}x2x10^{-12}}$

⇒ $\frac{6.6x10^{9}}{9.1x2}$

⇒ $0.3x10^{9}$

⇒ $36x10^{7} m/s$

ii. For calculation of Kinetic Energy or 'k.e.':

⇒ $k.e.= \frac{1}{2}m x (36x10^{7} x 36 x 10^{7)}$

⇒ $\frac{1}{2}x 9.1 x 10^{-31}x 1296 x 10^{14}$

⇒ $5896.8 x 10^{-17} m/s$

The group velocity is $36x10^{7} m/s$ and the Kinetic energy is $5896.8 x 10^{-17} m/s$.