Hydrogen (₁H¹), Deuterium (₁H²), singly ionised Helium (₂He⁴)⁺ and… | JEE Main 2014

Q62JEE Main 2014Medium

Transitions, Photon Emission & Excitation

Hydrogen $\left({}_{1}H^{1}\right)$ , Deuterium $\left({}_{1}H^{2}\right)$ , singly ionised Helium $\left({}_{2}He^{4}\right)^{+}$ and doubly ionised lithium $\left({}_{3}Li^{6}\right)^{++}$ all have one electron around the nucleus. Consider an electron transition from $n = 2$ to $n = 1.$ If the wavelengths of emitted radiation are $\lambda_{1}, \lambda_{2}, \lambda_{3}$ and $\lambda_{4}$ respectively then approximately which one of the following is correct?

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Answer: (c)

$\frac{1}{\lambda} = R Z^2 \left(1 - \frac{1}{4}\right)$ , so $\lambda \propto \frac{1}{Z^2}$ (nuclear mass effect neglected).
H and D: $Z = 1$ ; He $^+$ : $Z = 2$ ; Li $^{++}$ : $Z = 3$ .
$\lambda_1 = \lambda_2 = 4\lambda_3 = 9\lambda_4$
So the answer is (c).

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