Question

A moving electron has a de Broglie wave length of 7 x 10-7 m. calculate its kinetic energy. (Planck’s
constant = 6.626 x 10-34 Js, mass of an electron = 9.1 x 10-31 kg)

Answer 1

Answer:- Kinetic energy is $4.92*10^-^2^5J$

Solution:- De-Broglie wavelength equation is:

$\lambda =\frac{h}{p}$

where, h is planck's constant and $\lambda$ is the momentum.

We know that, $p=mv$

where, m is the mass in kg and $v$ is velocity .

Let's plug in $mv$ in place of p in the first equation:

$\lambda=\frac{h}{mv}$

Let's plug in the values in this equation:

$7*10^-^7m=\frac{6.626*10^-^3^4J.s}{9.1*10^-^3^1kg*v}$

Since, $J=kg.m^2.s^-^2$

So, $7*10^-^7m=\frac{6.626*10^-^3^4kg.m^2.s^-^1}{9.1*10^-^3^1kg*v}$

on rearranging the above equation:

$7*10^-^7m*9.1*10^-^3^1kg*v=6.626*10^-^3^4kg.m^2.s^-^1$

Now, we again rearrange this to solve for velocity as:

$v=\frac{6.626*10^-^3^4kg.m^2.s^-^1}{7*10^-^7m*9.1*10^-^3^1kg}$

$v=1.04*10^3m.s^-^1$

Now, we could calculate the kinetic energy using the formula:

$K.E=\frac{1}{2}mv^2$

$K.E=\frac{1}{2}9.1*10^-^3^1kg(1.04*10^3m.s^-^1)^2$

$K.E=4.92*10^-^2^5J$

So, the kinetic energy of the electron is $4.92*10^-^2^5J$ .

Answer 2

answer = 4.914× 10^(-37)