Question

The energy levels of certain atom are represented in the following figure. During the transition from 2E to E level, a photon of wavelength \(\lambda\) is emitted. The wavelength of photon produced during transition from \(\frac{4E}{3}\) level to E will be

• A. \(3\lambda\)
• B. \(\frac{\lambda }{3}\)
• C. \(\frac{3\lambda }{2}\)
• D. \(\frac{4\lambda }{3}\)

Hint:

The photon energy equals the gap between the two energy levels, and wavelength is inversely proportional to that gap.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
A photon emitted in a transition has energy equal to the difference between the two levels, \(\Delta E=\dfrac{hc}{\lambda}\).

Step 2: Energy gaps
From \(2E\) to \(E\), the gap is \(E\), so \(\lambda=\dfrac{hc}{E}\).
From \(\dfrac{4E}{3}\) to \(E\), the gap is \(\dfrac{E}{3}\).

Step 3: Calculation
\(\lambda'=\dfrac{hc}{E/3}=3\,\dfrac{hc}{E}=3\lambda\).

Final Answer:
The wavelength of the second photon is 3 times lambda, which is option (A). \[ \boxed{\text{(A) }3\lambda} \]