Singly charged gas ions are accelerated from rest through a

Singly charged gas ions are accelerated from rest through a voltage of 18.5 V. At what temperature will the average kinetic energy of gas molecules be the same as that given these ions?

Solution

Q V = gain in KE = 0.5 mv^2

at (T) kelvin, average velocity is
v = [3kT/m]^1/2
Average KE = 0.5 mv^2 = 0.5[3kT] = 3kT/2

3kT/2 = QV
T = (2 Q*18.5/k)
put value of k = boltzman constant = 1.23*10^-23 m² kg s^-2 K^-1
Q = charge on ion
T in Kelvin

T = 1.423 * 10^5 K