Question

Which of the following transition in hydrogen atom emits photon of highest frequency?

• A. \(n=5\) to \(n=2\)
• B. \(n=2\) to \(n=5\)
• C. \(n=2\) to \(n=3\)
• D. \(n=3\) to \(n=2\)

Hint:

Only downward transitions emit photons, and the largest energy gap gives the highest frequency.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
A photon is emitted only when an electron drops from a higher level to a lower level.
The emitted frequency satisfies \(h\nu=E_i-E_f\).

Step 2: Remove Absorption Cases
The transitions \(n=2\rightarrow5\) and \(n=2\rightarrow3\) go upward, so they absorb energy and emit nothing.

Step 3: Compare Emission Cases
\(E_n=-\dfrac{13.6}{n^{2}}\) eV.
For \(5\rightarrow2\): \(13.6\left(\dfrac{1}{4}-\dfrac{1}{25}\right)=2.86\) eV.
For \(3\rightarrow2\): \(13.6\left(\dfrac{1}{4}-\dfrac{1}{9}\right)=1.89\) eV.

Step 4: Result
The \(n=5\) to \(n=2\) transition has the larger energy, so it gives the highest frequency. This is option (A).

Final Answer:
The transition from n equal to 5 to n equal to 2 emits the highest frequency. \[ \boxed{\text{(A) }\text{n = 5 to n = 2}} \]