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Physics Case study (4 Marks)

Bohr’s Model and Physics of Atom · Uttarakhand Board (UBSE) STD 12 Science (Uttarakhand - English Medium). 2 questions.

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Case study (4 Marks)

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2 questions · self-marked practice — reveal the answer and mark yourself.

Question 14 Marks
When white radiation is passed through a sample of hydrogen gas at room temperature, absorption lines are observed in Lyman series only. Explain.
Answer
White radiations are x-rays that have energy ranging between 5-10eV.
When white radiation is passed through a sample of hydrogen gas at room temperature, absorption lines are observed only in the Lyman series.
At room temperature, almost all the atoms are in ground state.
The minimum energy required for absorption is 10.2eV (for a transition from n = 1 to n = 2).
The white radiation has photon radiations that have an energy of around 10.2 eV.
So, they are just sufficient to transmit an electron from n = 1 to n = 2 level.
Hence, the absorption lines are observed only in the Lyman series.
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Question 24 Marks
Suppose in an imaginary world the angular momentum is quantized to be even integral multiples of $\frac{\text{h}}{2\pi}$ What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model?
Answer
Even quantum numbers are allowed,
$\text{n}_1=2,\text{n}_2=4\xrightarrow{\ \ \ }$ For minimum energy or for longest possible wavelength.
$\text{E}=13.6\bigg(\frac{1}{\text{n}^2_1}-\frac{1}{\text{n}^2_2}\bigg)$
$\text{E}=13.6\Big(\frac{1}{2^2}-\frac{1}{4^2}\Big)=2.55$
$2.55=\frac{\text{hc}}{\lambda}$
$\lambda=\frac{\text{hc}}{2.55}=\frac{1242}{2.55}$
$\lambda=487.05\text{nm}=487\text{nm}$
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