JEE PYQ: Atomic Physics Question 2
Question 2 - 2021 (16 Mar Shift 1)
The first three spectral lines of H-atom in the Balmer series are given $\lambda_1, \lambda_2, \lambda_3$ considering the Bohr atomic model, the wave lengths of first and third spectral lines $\left(\frac{\lambda_1}{\lambda_3}\right)$ are related by a factor of approximately $x \times 10^{-1}$. The value of $x$, to the nearest integer, is ____.
Show Answer
Answer: 15
Solution
For 1st line: $\frac{1}{\lambda_1} = Rz^2\left(\frac{1}{2^2} - \frac{1}{3^2}\right) = Rz^2 \frac{5}{36}$. For 3rd line: $\frac{1}{\lambda_3} = Rz^2\left(\frac{1}{2^2} - \frac{1}{5^2}\right) = Rz^2 \frac{21}{100}$. So $\frac{\lambda_1}{\lambda_3} = \frac{21}{100} \times \frac{36}{5} = 1.512 = 15.12 \times 10^{-1}$, thus $x \approx 15$.
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