Modern Physics 1 Question 18

15. The largest wavelength in the ultraviolet region of the hydrogen spectrum is $122 nm$. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

(a) $802 nm$

(b) $823 nm$

(c) $1882 nm$

(d) $1648 nm$

$(2007,3$ M)

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Solution:

  1. The series in $U-V$ region is Lymen series. Longest wavelength corresponds to minimum energy which occurs in transition from $n=2$ to $n=1$.

$$ \therefore \quad 122=\frac{\frac{1}{R}}{\frac{1}{1^{2}}-\frac{1}{2^{2}}} $$

The smallest wavelength in the infrared region corresponds to maximum energy of Paschen series.

$$ \therefore \quad \lambda=\frac{\frac{1}{R}}{\frac{1}{3^{2}}-\frac{1}{\infty}} $$

Solving Eqs. (i) and (ii), we get

$$ \lambda=823.5 nm $$



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