Q11 / 50 · Manipal (MET) 2024 · Chemistry
The wave number of the shortest wavelength of absorption spectrum of hydrogen atom is _____ (Rydberg constant $\left.=109700 \mathrm{~cm}^{-1}\right)$.
Correct answer: 109700
Solution
Given, $R=109700 \mathrm{~cm}^{-1}$
Shortest wavelength mean transition is from infinity to $n=1$.
Using the formula,
$\begin{aligned}
& \bar{v}=R\left[\frac{1}{n_f^2}-\frac{1}{n_i^2}\right] \\
& n_t=\infty, n_i=n=1 \\
& \bar{v}=109700\left[\frac{1}{1}-\frac{1}{\infty}\right] \\
& \bar{v}=109700 \mathrm{~cm}^{-1}
\end{aligned}$
Hence, the correct answer is 109700.