Question

Calculate the temperature at which the average kinetic energy of a molecule of a gas will be same as that of an electron accelerated through 1 volt.

[Given: k_B = 1.4 × 10⁻² J/k, e = 1.6 × 10⁻¹⁹ C]

Answer 1

Given: k_B = 1.4 × 10⁻² J/k,

e = 1.6 × 10⁻¹⁹ C

V = 1 volt

The kinetic energy (KE) of an electron accelerated through a potential difference of 1 volt is given by the equation:

KE = e . V

= 1.6 × 10⁻¹⁹ C × 1 V

= 1.6 × 10⁻¹⁹ J

The average kinetic energy of a molecule of an ideal gas is given by the formula:

KE = `3/2 k_BT`

1.6 × 10⁻¹⁹ J = `3/2 k_B T`

T = `(1.6 xx 10^-19 xx 2)/(3 * k_B)`

= `(2 xx 1.6 xx 10^-19)/(3 xx 1.4 xx 10^-23)`

= `(3.2 xx 10^-19)/(4.2 xx 10^-23)`

= 7619.05 K