Question

An electron is moving at a speed of c/100. find its deBroglie wavelength and frequency. Neglect relativistic effects.

Answer 1

Answer:

DeBroglie wavelength is $2.42\times 10^{-10}\ m$

Frequency is $1.24\times 10^{16}\ Hz$

Explanation:

Mass of electron = 9.10938356 × 10⁻³¹ kg

Planck's constant = h = 6.626 × 10⁻³⁴ m²kg/s

Speed of light = c = 3×10⁸ m/s

$\lambda=\frac{h}{p}=\frac{h}{mv}\\\Rightarrow \lambda=\frac{6.626\times 10^{-34}}{9.10938356\times 10^{-31}\times \frac{3\times 10^8}{100}}\\\Rightarrow \lambda=2.42\times 10^{-10}\ m$

DeBroglie wavelength is $2.42\times 10^{-10}\ m$

$v=f\lambda\\\Rightarrow f=\frac{v}{\lambda}\\\Rightarrow \frac{\frac{3\times 10^8}{100}}{2.42\times 10^{-10}}\\\Rightarrow f=1.24\times 10^{16}\ Hz$

Frequency is $1.24\times 10^{16}\ Hz$

Answer 2

Answer:

$\lambda=2.42\times 10^{-10}\ m$

$\nu=1.24\times 10^{18}\ s^{-1}$

Explanation:

The expression for the deBroglie wavelength is:

$\lambda=\frac {h}{m\times v}$

Where,

$\lambda$ is the deBroglie wavelength

h is Plank's constant having value $6.626\times 10^{-34}\ Js$

m is the mass of electron having value $9.11\times 10^{-31}\ kg$

v is the speed of electron.

Given that v = c / 100

Where, c is the speed of light having value $3\times 10^8\ m/s$

Thus, v = $\frac {3\times 10^8}{100}\ m/s=3\times 10^6\ m/s$

Applying in the equation as:

$\lambda=\frac {h}{m\times v}$

$\lambda=\frac {6.626\times 10^{-34}}{9.11\times 10^{-31}\times 3\times 10^6}\ m$

$\lambda=\frac{10^{-34}\times \:6.626}{10^{-25}\times \:27.33}\ m$

$\lambda=\frac{6.626}{10^9\times \:27.33}\ m$

$\lambda=2.42\times 10^{-10}\ m$

Also,

$\nu=\frac {c}{\lambda}$

So,

$\nu=\frac {3\times 10^8}{2.42\times 10^{-10}}\ s^{-1}$

$\nu=\frac{10^{18}\times \:3}{2.42}\ s^{-1}$

$\nu=1.24\times 10^{18}\ s^{-1}$