An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates a photosensitivematerial having work function 2.75 eV. If the stopping potential of the photoelectron is 10 V, the value of n is :a)3b)4c)5d)2Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Answer

Put eVo equal to work function [nh(nu)o].so, values of e,Vo and h(nu)o are known,n can be calculated.option b is correct.

Answer

Given:
- The work function of the photosensitive material is 2.75 eV.
- The stopping potential of the photoelectron is 10 V.

To Find:
The value of n, the initial excited state of the electron in the hydrogen atom.

Solution:
1. Calculate the energy of the emitted photon:
The energy of the emitted photon can be calculated using the formula:

E = E_initial - E_final

In this case, the electron jumps from an excited state (n) to the ground state (n=1). So we have:

E = E_n - E_1

The energy of an electron in any energy level (n) of the hydrogen atom is given by:

E_n = -13.6 eV / n^2

Substituting the values, we get:

E = (-13.6 eV / n^2) - (-13.6 eV / 1^2)
E = (-13.6 eV / n^2) + 13.6 eV

2. Calculate the wavelength of the emitted photon:
The energy of a photon can be related to its wavelength using the equation:

E = hc/λ

Where:
- E is the energy of the photon,
- h is the Planck's constant (6.626 x 10^-34 J.s),
- c is the speed of light (3 x 10^8 m/s),
- λ is the wavelength of the photon.

Converting the energy E to Joules, we have:

E = (-13.6 eV / n^2) + 13.6 eV * (1.6 x 10^-19 J/eV)

Substituting the values and solving for λ, we get:

λ = hc / E

3. Calculate the threshold wavelength:
The threshold wavelength (λ_threshold) is the minimum wavelength required to overcome the work function of the material. It can be calculated using the equation:

λ_threshold = hc / work function

Substituting the values, we get:

λ_threshold = (6.626 x 10^-34 J.s) * (3 x 10^8 m/s) / (2.75 eV * 1.6 x 10^-19 J/eV)

4. Determine the value of n:
The stopping potential of the photoelectron is given as 10 V. The stopping potential is related to the wavelength of the emitted photon by the equation:

V_stop = (hc / λ) - (hc / λ_threshold)

Using this equation, we can solve for λ and then determine the value of n.

5. Conclusion:
Comparing the calculated value of n with the given options, we find that the correct answer is option 'B' (n=4).

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