Photons of energy 12eV are incident on a metal. It is found that current flows from the metal until a stopping potential of 8.0V is applied.

What would happen if the wavelength of the incident photons was tripled?

Would the energy be 4eV,so 12/3=4, and there will be no current flow? Is this correct? Please help!Thank you.

When photons of energy 12 eV are incident on a metal, they transfer their energy to the electrons in the metal, causing them to be emitted from the surface, a phenomenon known as the photoelectric effect. The energy of a photon is related to its wavelength by the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.

In the given situation, the stopping potential applied to the metal is 8.0 V. This means that in order to prevent the emitted electrons from reaching the positive electrode and producing a current, an electric potential difference of 8.0 V is required. This stopping potential is a measure of the maximum kinetic energy the emitted electrons can have without crossing the gap and producing a current.

Now, let's consider what would happen if the wavelength of the incident photons was tripled. From the equation E = hc/λ, it follows that when the wavelength is tripled, the energy of the photons would be reduced to one-third of the original value. Therefore, the energy of the incident photons would become 4 eV, as you correctly calculated (12 eV / 3 = 4 eV).

If the energy of the incident photons is reduced to 4 eV, it means that each photon carries less energy compared to the previous case. As a result, the electrons emitted from the metal would have less energy, and therefore, their maximum kinetic energy would also be reduced. Consequently, a lower stopping potential would be required to prevent the emitted electrons from producing a current.

Since the stopping potential applied in this scenario is 8.0 V, which is higher than the reduced energy of the emitted electrons (4 eV), there would still be current flow. The electrons would still have sufficient energy to overcome the potential barrier and reach the positive electrode, resulting in a measurable current.

Therefore, in summary, if the wavelength of the incident photons is tripled, the energy of the incident photons would be reduced to 4 eV, and there would still be current flow because the stopping potential applied is higher than the reduced energy of the emitted electrons.