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:
- 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
$$ \lambda=823.5 nm $$
