The Photoelectric Effect

The photoelectric effect refers to the emission of electrons from a material when it is exposed to electromagnetic radiation, such as light. This phenomenon was first explained by Albert Einstein in 1905 and has since played a significant role in our understanding of quantum physics.

Work Function

The work function of a metal is the minimum energy required to remove an electron from its surface. It can be thought of as the energy barrier that needs to be overcome for the photoelectric effect to occur. The work function is typically measured in electron volts (eV).

In this case, the work function of the metal is given as 4 eV. This means that at least 4 eV of energy is required to liberate an electron from the metal's surface.

Wavelength of Light

The wavelength of light incident on the metal is given as 5000 Å (angstroms). To determine if the photoelectric effect will occur, we need to consider the relationship between the energy of the incident photons and the work function.

Energy of Photons

The energy of a photon can be calculated using the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength of the light.

Using this equation, we can find the energy of the photons corresponding to a wavelength of 5000 Å:

E = (6.626 x 10^-34 J·s) * (3 x 10^8 m/s) / (5000 x 10^-10 m)
E ≈ 3.9768 x 10^-19 J

Converting this energy to electron volts:

1 eV = 1.6 x 10^-19 J
E ≈ 3.9768 x 10^-19 J / (1.6 x 10^-19 J/eV)
E ≈ 2.486 eV

Comparison

Comparing the energy of the incident photons (2.486 eV) to the work function of the metal (4 eV), we can determine whether the photoelectric effect will occur.

Since the energy of the photons is less than the work function, the incident light does not possess enough energy to overcome the energy barrier and liberate electrons from the metal's surface. Hence, no photoelectric effect will occur in this scenario.

Conclusion

In conclusion, when light with a wavelength of 5000 Å is incident on a metal with a work function of 4 eV, there will be no photoelectric effect. The energy of the incident photons is insufficient to overcome the energy barrier required to liberate electrons from the metal's surface.

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