Question

When an electron in the hydrogen atom in ground state absorbs a photon of energy $12.1eV$, its angular moment-rum

• A. decreases by $2.11\times {10}^{-34}Js$
• B. decreases by $1.055\times {10}^{-34}Js$
• C. increases by $2.11\times {10}^{-34}Js$
• D. increases by $1.055\times {10}^{-34}Js$

Answer 1

The correct option is C increases by $2.11\times {10}^{-34}Js$

$\begin{array}{c}\text{Given,}\\ \text{when hydrogen atom absorb energy}=12.1\text{ev}\\ \text{then it's excites from ground state to}\\ {\text{2}}^{nd}\text{excited state or}{3}^{rd}\text{energy level}\\ \text{because}\end{array}$

$\begin{array}{cc}{E}_3-E_1& =-1.51-(-13.6)\\ & =12.1ev\end{array}$

$\text{Now,}$

$\text{Angular momentam of}{e}^{-}=\frac{nh}{2\pi }$

$\begin{array}{c}\text{In ground state}(n=1)\\ AM=\frac{h}{2\pi }\\ \text{In excited state}(n=3)\\ AM=\frac{3h}{2\pi }\end{array}$

$\begin{array}{cc}\text{increase in}AM& =\frac{3h}{2\pi }-\frac{h}{2\pi }\\ & =\frac{h}{\pi }\\ & =\frac{6.6\times {10}^{-34}}{3.14}\\ & =2.11\times {10}^{-34}Js\end{array}$