Question

What is the order of the temperature at which average kinetic energy of an atom in gaseous hydrogen becomes equal to the binding energy of the electron in hydrogen atom?

• A. ${10}^4$ K
• B. ${10}^5$ K
• C. ${10}^3$ K
• D. ${10}^2$ K

Answer 1

The correct option is B ${10}^5$ K

Let the temperature be $T$.

So, the K.E. of an atom is gaseous hydrogen is $3kT/2$

where $k=1.38\times {10}^{-23}$ is the boltzmann constant.

Now the binding energy of the electron in hydrogen atom is $13.6eV=13.6\times 1.6\times {10}^{-19}J$

Equating Binding energy and the kinetic energy we get,

$T=1.004\times {10}^{5}K$

So temperature is of order of ${10}^{5}K$