Question

The average translational kinetic energy of a molecule in a gas is 'E₁'. The kinetic energy of the electron (e) accelerated from rest through p.d. 'V' volt is 'E₂'. The temperature at which E₁ = E₂ is possible, is ______.

विकल्प

• `(2"VNe")/(3"R")`

• `(3"VNe")/(2"R")`

• `("VNe")/("R")`

• `(2"VNe")/(2"R")`

Answer 1

The average translational kinetic energy of a molecule in a gas is 'E₁'. The kinetic energy of the electron (e) accelerated from rest through p.d. 'V' volt is 'E₂'. The temperature at which E₁ = E₂ is possible, is `underline((2"VNe")/(3"R"))`.

Explanation:

`"E"_1=3/2"kT"`       for a molecule

E₂ = eV      for an electron accelerated through potential difference V

As per condition E₁ = E₂

`therefore3/2"kT"="eV"`

`T=2/3*"eV"/"k"`

Now, R = Nk

where

k = Boltzmann constant

R = Universal constant

N = Avogadro's number

`thereforeT=2/3*"N"/"R""eV"`