NEET · Chemistry · STD 11 - 2. structure of atom
The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes \(n =2 \rightarrow n =3\) and \(n =4 \rightarrow n =6\) transitions, respectively, is
- A \(\frac{1}{36}\)
- B \(\frac{1}{16}\)
- C \(\frac{1}{9}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\(\frac{1}{\lambda}=RZ^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right) \)
\( \text {For } 2 \rightarrow 3 \Rightarrow \frac{1}{\lambda_1}=R \times(1)^2\left(\frac{1}{2^2}-\frac{1}{3^2}\right) \ldots\text{(1)} \)
\( \text {For } 4 \rightarrow 6 \Rightarrow \frac{1}{\lambda_2}=R \times(1)^2\left(\frac{1}{4^2}-\frac{1}{6^2}\right) \ldots\text{(2)}\)
Divide (1) & (2)
\(\frac{\lambda_2}{\lambda_1}=\frac{\frac{1}{2^2}-\frac{1}{3^2}}{\frac{1}{4^2}-\frac{1}{6^2}} \)
\( \frac{\lambda_2}{\lambda_1}=\frac{4}{1} \)
\( \therefore \frac{\lambda_1}{\lambda_2}=\frac{1}{4}\)
\( \text {For } 2 \rightarrow 3 \Rightarrow \frac{1}{\lambda_1}=R \times(1)^2\left(\frac{1}{2^2}-\frac{1}{3^2}\right) \ldots\text{(1)} \)
\( \text {For } 4 \rightarrow 6 \Rightarrow \frac{1}{\lambda_2}=R \times(1)^2\left(\frac{1}{4^2}-\frac{1}{6^2}\right) \ldots\text{(2)}\)
Divide (1) & (2)
\(\frac{\lambda_2}{\lambda_1}=\frac{\frac{1}{2^2}-\frac{1}{3^2}}{\frac{1}{4^2}-\frac{1}{6^2}} \)
\( \frac{\lambda_2}{\lambda_1}=\frac{4}{1} \)
\( \therefore \frac{\lambda_1}{\lambda_2}=\frac{1}{4}\)
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