Question

Let \(\lambda_L\) and \(\lambda_S\) be the longest and shortest wavelength photons in the Balmer series respectively. Find \(\frac{\lambda_L}{\lambda_S}\):

• A. \( \frac{9}{5} \)
• B. 2
• C. \( \frac{5}{2} \)
• D. \( \frac{8}{3} \)

Hint:

In hydrogen spectrum, longest wavelength corresponds to smallest energy transition.

Answer 1

The Correct Option is A

Step 1: Balmer formula.
1/λ = R(1/2² - 1/n²).

Step 2: Longest wavelength transition.
n=3 → 2: 1/λ_L = R(1/4 - 1/9) = R(5/36).

Step 3: Shortest wavelength transition.
n=∞ → 2: 1/λ_S = R(1/4 - 0) = R/4.

Step 4: Forming the ratio.
λ_L/λ_S = (4)/(5/36) = 144/5? Wait, correct: λ_L/λ_S = (36/5R)/(4/R) = 36/5 × 1/4 = 9/5.

Step 5: Conclusion.
The ratio of longest to shortest wavelength is 9/5.