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JEE Main 2020 (9 Jan, Shift 2) · Transitions, Photon Emission & Excitation

Transitions, Photon Emission & Excitation question from JEE Main 2020 (9 Jan, Shift 2)

Q51JEE Main 2020 · 9 JAN · SHIFT 2Medium

Transitions, Photon Emission & Excitation

The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state?

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Answer: (b)

Ionisation energy $= Z^2 \times 1$ Ry $= 9$ Ry $\Rightarrow Z = 3$ .
Second excited state is $n = 3$ : $E = 9 \times 13.6 \times \left(1 - \frac{1}{9}\right) = 108.8$ eV
$\lambda = \frac{1240}{108.8}$ nm $= 11.4$ nm
So the answer is (b) 11.4 nm.

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