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Spacing between energy levels n = 1 and n = 2 in hydrogen atom is greater than that of n = 2 and n = 3

Spacing between energy levels n = 1 and n = 2 in hydrogen atom is equal to that n = 2 and n = 3

Spacing between energy levels n = 1 and n = 3 in hydrogen atom less than that of n = 2 and n = 3

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answer is A.

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Detailed Solution

$\begin{array}{l} E_{n} = - \frac{13 .6 Z^{2}}{n^{2}} eV \\ {ΔE}_{1 \to 2} = - \frac{13 .6}{2^{2}} + \frac{13 .6}{1^{2}} = 10 .2 eV \\ {ΔE}_{2 \to 3} = - \frac{13 .6}{3^{2}} + \frac{13 .6}{2^{2}} = 1.9 eV \end{array}$

$∴$ On moving from lower value of n to higher value of n energy difference between successive energy levels decreases.

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