Physics question!?

Question

singly charged gas ions are accelerated from rest through a voltage of 13.0 V. At what temperature will the average kinetic energy of gas molecules be the same as that given these ions?

Answer 1

Q V = gain in KE = 0.5 mv^2

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at (T) kelvin, average velocity is

v = [3kT/m]^1/2

Average KE = 0.5 mv^2 = 0.5[3kT] = 3kT/2

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equating

3kT/2 = QV

T = (2 Q*13/k)

put value of k = boltzman constant

Q = charge on ion

T in Kelvin