Question

What is the wave number of lowest transition associated with Paschen series?

• A. \(\overset{̄}{v} = R_H(\frac{5}{36}) \text{cm}^{-1}\)
• B. \(\overset{̄}{v} = R_H(\frac{36}{5}) \text{cm}^{-1}\)
• C. \(\overset{̄}{v} = R_H(\frac{144}{7}) \text{cm}^{-1}\)
• D. \(R_H(\frac{7}{144}) \text{cm}^{-1}\)

Hint:

Paschen series ends at n = 3, and its lowest-energy line is the transition from n = 4 to n = 3.

Answer 1

The Correct Option is D

Step 1: Setup:
Paschen lines all land on $n=3$. Energy released grows as the starting level rises, so the weakest line starts from $n=4$.

Step 2: Compute:
Wave number is $R_H\,(1/9 - 1/16)$. Using the common denominator 144 gives $16/144 - 9/144 = 7/144$.

Step 3: Compare Options:
Option (A), $5/36$, is $1/4 - 1/9$, a Balmer line. Options (B) and (C) are inverted fractions. Option (D) is the only one equal to $7/144$.

Final Answer:
The wave number is $R_H \times 7/144$, option (D). \[ \boxed{\text{(D) } R_H\left(\tfrac{7}{144}\right)\text{cm}^{-1}} \]