Question

To what effective potential a proton beam be subjected to give its protons a wavelength of 1 * 10-10m.

Answer 1

Answer:A potential of $1.986\times 10^{-17} joules$ will required to give a proton a wavelength of $1\times 10^{-10}$ m.

Solution:

$\lambda =1\times 10^{-10}m$

$h=\text{Planck's constant}={6.62\times 10^{-34}J s ,c=\text{speed of light}=3\times 10^{8}m/s$

$E=\frac{hc}{\lambda }$ (Planck's equation)

$E=\frac{6.62\times 10^{-34}J s\times 3\times 10^{8}m/s}{1\times 10^{-10}m}$

$E= 19.86\times 10^{-16} joules=1.986\times 10^{-17} joules$

A potential of $1.986\times 10^{-17} joules$ will required to give a proton a wavelength of $1\times 10^{-10}$ m.

Answer 2

Given:

Wavelength = 1 *10^-10

To find:

Effective potential.

Solution:

By Planck's equation,

Effective potential = Planck's constant * Speed of the light / Wavelength

Here,

Planck's constant - 6.62 * 10^-34

Speed of light = 3 * 10^8

Substituting,

We get,

6.62 * 10^-34 * 3 * 10^8 / 1 * 10^-10

Effective potential = 1.968 * 10^-17 J