JEE MAIN - Physics (2022 - 25th July Evening Shift - No. 17)
Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $$\lambda$$. The value of principal quantum number '$$n$$' of the excited state will be : ($$\mathrm{R}:$$ Rydberg constant)
$$\sqrt{\frac{\lambda \mathrm{R}}{\lambda-1}}$$
$$\sqrt{\frac{\lambda \mathrm{R}}{\lambda \mathrm{R}-1}}$$
$$\sqrt{\frac{\lambda}{\lambda \mathrm{R}-1}}$$
$$\sqrt{\frac{\lambda R^{2}}{\lambda R-1}}$$
Explanation
$$\because$$ $${1 \over \lambda } = R\left( {{1 \over {{1^2}}} - {1 \over {{n^2}}}} \right)$$
$$ \Rightarrow {1 \over {\lambda R}} = 1 - {1 \over {{n^2}}}$$
$$ \Rightarrow {1 \over {{n^2}}} = 1 - {1 \over {\lambda R}} = {{\lambda R - 1} \over {\lambda R}}$$
$$ \Rightarrow n = \sqrt {{{\lambda R} \over {\lambda R - 1}}} $$
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