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Physics · 2022 · 3 marks
CBSE 2022 · Region 2 · Set 2 · Q9
(a) State Bohr's quantization condition for defining stationary orbits. (b) Use the energy level diagram shown below to obtain the relation between…
(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 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.