Photoelectric Effect Problems

The photoelectric effect is the phenomenon in which electrons are emitted from a metal surface when light falls on it. This effect is important in the field of quantum mechanics and has many practical applications. Here are some photoelectric effect problems that can help you understand the concept better.

1. What is the maximum kinetic energy of an electron emitted by a sodium metal surface when it is exposed to light of wavelength 500 nm?

Solution:
The work function of sodium metal is 2.28 eV. The energy of a photon of 500 nm wavelength is given by E = hc/λ, where h is Planck's constant and c is the speed of light. Substituting the values, we get E = (6.626 x 10^-34 J s)(3 x 10^8 m/s)/(500 x 10^-9 m) = 3.97 x 10^-19 J. The maximum kinetic energy of the electron can be found using the equation Kmax = E - Φ, where Φ is the work function. Substituting the values, we get Kmax = 3.97 x 10^-19 J - 2.28 eV = 1.69 x 10^-19 J.

2. What is the threshold frequency for a metal whose work function is 4.5 eV?

Solution:
The threshold frequency is the minimum frequency of light required to eject an electron from a metal surface. It can be calculated using the equation f = Φ/h, where Φ is the work function and h is Planck's constant. Substituting the values, we get f = 4.5 eV/h = (4.5 x 1.6 x 10^-19 J)/6.626 x 10^-34 J s = 6.80 x 10^14 Hz.

3. What is the stopping potential for a metal whose work function is 2.3 eV when it is exposed to light of frequency 5.0 x 10^15 Hz?

Solution:
The stopping potential is the minimum voltage required to stop the flow of electrons emitted from a metal surface when it is exposed to light. It can be calculated using the equation Vstop = hf/e - Φ/e, where h is Planck's constant, f is the frequency of light, e is the charge of an electron, and Φ is the work function. Substituting the values, we get Vstop = (6.626 x 10^-34 J s)(5.0 x 10^15 Hz)/(1.6 x 10^-19 C) - 2.3 eV/(1.6 x 10^-19 C) = 1.36 V.

Conclusion:
The photoelectric effect is an important concept in quantum mechanics and has many practical applications. By solving problems related to the photoelectric effect, you can develop a better understanding of the concept and its applications.

Thank you so much