Singly charged gas ions are accelerated from rest through a voltage of 10.3 V. At what temperature (in K) will the average kinetic energy of gas molecules be the same as that given these ions?

Temperature of the gas molecules is 7.96 x 10⁴ K

Explanation:

Given :

Ions accelerated through voltage, V = 10.3 volts

The work done to change the position of singly charged gas ions is given by the relation :

W = q x V

Here q is charge of the ions and its value is 1.6 x 10⁻¹⁹ C.

Average kinetic energy of gas molecules is given by the relation:

K.E. =

Here T is temperature and k is Boltzmann constant and its value is 1.38 x 10⁻²³ J/K.

According to the problem, the average kinetic energy of gas is equal to the work done to move the singly charged ions, i.e. ,

K.E. = W

Rearrange the above equation in terms of T :

Substitute the suitable values in the above equation.

T = 7.96 x 10⁴ K