First slide

Hydrogen spectrum

Question

In a hydrogen atom, the electron is in $n^{t h}$ excited state. It comes down to the first excited state by emitting 10 different wavelengths. The value of n is

Moderate

A

6
B

7
C

8
D

9

Solution

Number of possible emission lines are n(n - 1)/2 when an electron jumps from $n^{t h}$ state to ground state. In this question, this value should be (n - 1) (n - 2)/2.
Hence, $10 = \frac{(n - 1) (n - 2)}{2}$
Solving this, we get n = 6.

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