CBSE 2022 · Region 2 · Set 2 · Q9 · 3 marks
(a)State Bohr's quantization condition for defining stationary orbits.(b)Use the energy level diagram shown below to obtain the relation between three wavelengths $\displaystyle \lambda_{1}, \lambda_{2}$ and $\displaystyle \lambda_{3}$ emitted due to the transition of electron from the energy states C and B.
(a)
State Bohr's quantization condition for defining stationary orbits.
(b)
Use the energy level diagram shown below to obtain the relation between three wavelengths $\displaystyle \lambda_{1}, \lambda_{2}$ and $\displaystyle \lambda_{3}$ emitted due to the transition of electron from the energy states C and B.
Marking-scheme solution
(a)
Bohr's Quantization condition for stationary orbit
(b)
Relation between $\displaystyle \lambda_{1}, \lambda_{2}$ and $\displaystyle \lambda_{3}$
(a)
Condition for stationary orbits:- The electron revolves around the nucleus only in those orbits for which angular momentum is some integral multiple of $\displaystyle \frac{h}{2 \pi}$.
$$\mathrm{mvr}=\mathrm{L}=\frac{n h}{2 \pi r}
$$(b) For transition
$$C \rightarrow A
$$\frac{h c}{\lambda_{$\displaystyle 3$}}=E_{C}-E_{A}
$$For transition
$$C \rightarrow B
$$\frac{h c}{\lambda_{$\displaystyle 1$}}=E_{C}-E_{B}
$$For transition $\displaystyle B \rightarrow A \quad \frac{h c}{\lambda_{2}}=E_{B}-E_{A}$
$$\begin{aligned}
\Rightarrow & E_{C}-E_{A}=E_{C}-E_{B}+E_{B}-E_{A}
& \frac{1}{\lambda_{$\displaystyle 3$}}=\frac{1}{\lambda_{$\displaystyle 1$}}+\frac{1}{\lambda_{$\displaystyle 2$}}
\end{aligned}
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CBSE Class 12 Physics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.