X different wavelengths

Question:

$X$ different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number $\mathrm{n}=6$ ? The value of $\mathrm{X}$ is

Solution:

No. of different wavelengths $=\frac{\mathrm{n}(\mathrm{n}-1)}{2}$

$=\frac{6 \times(6-1)}{2}=\frac{6 \times 5}{2}=15$

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