Question

The first excited state of hydrogen atom is higher to its ground energy level by $10.2eV$. The temperature necessary to excite hydrogen atom to first excited state will be

• A. $0.88K$
• B. $7.88\times {10}^{2}K$
• C. $7.88\times {10}^{3}K$
• D. $7.88\times {10}^{4}K$

Answer 1

The correct option is D $7.88\times {10}^{4}K$

Energy required by hydrogen atom to excite electron from ground level to higher level:

$=10.2eV=10\times 1.6\times {10}^{-19}=1.6\times {10}^{-18}J$

Let $T$ be the required temperature

Kinetic energy of the electron $=$ energy required to excite

$\frac{3}{2}kT=1.6\times {10}^{-18}T=\frac{2\times 1.6\times {10}^{-18}}{3\times 1.38\times {10}^{-23}}=7.88\times {10}^{2}K$