Question

In Bohr model, electron transitions from $n=5$ to $n=1$ emit wavelength $\lambda$. What is wavelength for transition $n=5$ to $n=2$?

• A. $\frac{8}{7}\lambda$
• B. $\frac{24}{7}\lambda$
• C. $\frac{16}{7}\lambda$
• D. $\frac{32}{7}\lambda$

Hint:

Always use energy difference proportionality for Bohr transitions, not raw wavelength formulas.

Answer 1

The Correct Option is C

Concept: Bohr wavelength relation: \[ \frac{1}{\lambda} \propto \left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right) \]

Step 1: First transition For $5 \to 1$: \[ \frac{1}{\lambda} \propto \left(1 - \frac{1}{25}\right) = \frac{24}{25} \]

Step 2: Second transition For $5 \to 2$: \[ \frac{1}{\lambda'} \propto \left(\frac{1}{4} - \frac{1}{25}\right) = \frac{25 - 4}{100} = \frac{21}{100} \]

Step 3: Ratio \[ \frac{\lambda'}{\lambda} = \frac{24/25}{21/100} \] \[ = \frac{24}{25} \cdot \frac{100}{21} = \frac{96}{21} = \frac{32}{7} \]

Step 4: Final result \[ \lambda' = \frac{32}{7}\lambda \] Final Answer: \[ \boxed{(D)} \]