A beam of monochromatic light is used to excite the electron in Li++… | JEE Main 2022 (27 Jun, Shift 1)

Q43JEE Main 2022 · 27 JUN · SHIFT 1Medium

Transitions, Photon Emission & Excitation

A beam of monochromatic light is used to excite the electron in Li++ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be x $\times$ 10 $-$ 10 m. The value of x is ___________.

[Given hc = 1242 eV nm]

Numerical answer type. Work it out, then open the answer.

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Answer: 114

For Li $^{++}$ , $Z = 3$ : $\Delta E = 13.6 \times 9 \times \left(1 - \frac{1}{9}\right) = 108.8$ eV
$\lambda = \frac{hc}{\Delta E} = \frac{1242}{108.8}$ nm $= 11.4$ nm
$\lambda = 114 \times 10^{-10}$ m, so $x = 114$ .

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