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  • A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be :Option: 1 2<

A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be :

Option: 1

2


Option: 2

3


Option: 3

4


Option: 4

1


Answers (1)

best_answer

\begin{aligned} & 12.5=-13.6\left[\frac{1}{\mathrm{n}_{\mathrm{f}}^2}-\frac{1}{\mathrm{n}_{\mathrm{i}}^2}\right] \quad \mathrm{ni}=1 \\ & 12.5=-13.6\left[\frac{1}{\mathrm{n}_{\mathrm{f}}^2}-1\right] \\ & 12.5=13.6-\frac{13.6}{\mathrm{n}_{\mathrm{f}}^2} \\ & -1.1=-\frac{13.6}{\mathrm{n}_{\mathrm{f}}^2} \\ & \mathrm{n}_{\mathrm{f}} \simeq 3.5 \\ & \mathrm{n}_{\mathrm{f}}=3 \quad \text { so transition is } 3 \text { to } 1 \\ & \text { No. of lines } \left.={ }^3 C_2 \quad{ }^n C_r=\frac{\underline{n}}{|(n-r)| r}\right) \\ & =\frac{\lfloor 3}{\lfloor(3-2)(\lfloor 2]} \\ & \frac{3 \times 2 \times 1}{1 \times 2}=3 \text { lines } \\ & \end{aligned}

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