## Calculate the ratio of the kinetic energy of an electron to that of a proton if their wavelengths are equal. Assume that the speeds are nonr

Question

Calculate the ratio of the kinetic energy of an electron to that of a proton if their wavelengths are equal. Assume that the speeds are nonrelativistic.

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3 years 2021-08-30T13:31:01+00:00 2 Answers 66 views 0

## Answers ( )

1. Answer:

the ratio of the kinetic energy of an electron to that of a proton if their wavelengths are equal is 1835.16 .

Explanation:

We know, wavelength is expressed in terms of Kinetic Energy by :

Therefore ,

It is given that both electron and proton have same wavelength.

Therefore,

…. equation 1.

…. equation 2.

Now, dividing equation 1 by 2 .

We get ,

Putting value of mass of electron = and mass of proton =

We get :

Hence , this is the required solution.

2. Answer:

Explanation:

Given that the wavelengths of electron and proton are equal at non- relativistic speed.

From De-Broglie wave equation we know that:

where:

wavelength

Planck’s constant

linear momentum of  the particle

Then’

…………………………….(1)

we’ve mass of electron,

mass pf proton,

Now,

kinetic energy of electron:

kinetic energy of proton:

So,

from eq. (1)