Question

If the electron in hydrogen atom jumps from third Bohr orbit to ground state directly and the difference between energies of the two states is radiated in the form of photons. If the work function of the material is 4.1 eV , then stopping potential is nearly

[Energy of electron in \(n^{\text {th }}\) orbit \(=\frac{-13 \cdot 6}{n^2} \mathrm{eV}\) ]

• A. 3 V
• B. 4 V
• C. 6 V
• D. 8 V

Hint:

Find the photon energy from the n=3 to n=1 transition, subtract the work function and divide by the electron charge.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Einstein's equation gives \(eV_0=E_{photon}-\phi\).

Step 2: Photon energy
\(E_3=-\dfrac{13.6}{9}=-1.51\ \text{eV}\) and \(E_1=-13.6\ \text{eV}\).
\(E_{photon}=13.6-1.51=12.09\ \text{eV}\).

Step 3: Stopping potential
\(eV_0=12.09-4.1=7.99\ \text{eV}\).
\(V_0\approx 8\ \text{V}\).

Step 4: Compare the options
The nearest value is option (D).

Final Answer:
The stopping potential is about 8 V. \[ \boxed{\text{(D) }8\ \text{V}} \]