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At what temperature linear kinetic energy of a gas molecule will be equal to that of the electron accelerated through potential difference of 10V.

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 As we know that charge of an electron is given by (q) = 1.6 x 10-19 C
The potential difference is given here (V) = 10 V

KEelectron = q x V = 1.6 x 10-19 x 10 = 1.6 x 10-18

Linear Kinetic Energy of a gas is given by 3/2 KT where K is Boltzman constant(R/N = 1.38 x 10-23)
KEGas = 3/2 (1.38 x 10-23)(T)

Now we equate both the equation:

3/2 (1.38 x 10-23)(T) = 1.6 x 10-18
T = 7.72 x 105 K

At 7.72 x 105 K temperature linear kinetic energy of a gas molecule will be equal to that of the electron.

 

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