MHT CET · Physics · Atomic Physics
Frequency of the series limit of Balmer series of hydrogen atom in terms of Rydberg's constant (R) and velocity of light (c) is
- A \(4 \mathrm{Rc}\)
- B \(\frac{4}{\mathrm{Rc}}\)
- C \(\mathrm{Rc}\)
- D \(\frac{\mathrm{Rc}}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{\mathrm{Rc}}{4}\)
Step-by-step Solution
Detailed explanation
Wavelength of Balmer series is given as, \(\frac{1}{\lambda}=\mathrm{R}\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right)\) where \(\mathrm{n}_1=2\)
For series limit, \(\mathrm{n}_2=\infty\)
\(
\therefore \frac{1}{\lambda}=\mathrm{R}\left(\frac{1}{4}-\frac{1}{\infty}\right)=\mathrm{R}\left(\frac{1}{4}\right)
\)
Now, \(v=\frac{c}{\lambda}\)
\(
\therefore v=\frac{R c}{4}
\)
For series limit, \(\mathrm{n}_2=\infty\)
\(
\therefore \frac{1}{\lambda}=\mathrm{R}\left(\frac{1}{4}-\frac{1}{\infty}\right)=\mathrm{R}\left(\frac{1}{4}\right)
\)
Now, \(v=\frac{c}{\lambda}\)
\(
\therefore v=\frac{R c}{4}
\)
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