During the photoelectric effect, when photons strike with 5.1eV, electrons emitted from which metal have higher kinetic energy? Metal Na Ag Work function 2.3 eV 4.3 eV

Question

During the photoelectric effect, when photons strike with 5.1eV, electrons emitted from which metal have higher kinetic energy?

Metal

Answer 1

The kinetic energy of electrons emitted during the photoelectric effect depends on both the energy of the incoming photons and the work function of the metal. The work function is the minimum energy required to release an electron from the metal's surface. If the photon energy is greater than the work function, the excess energy is converted into the kinetic energy of the emitted electrons.

Calculation:

The kinetic energy ($K.E.$) of the emitted electrons is given by the formula:

K.E.=Ephoton−ϕK.E. = E_{\text{photon}} - \phiK.E.=Ephoton​−ϕ

where:

• EphotonE_{\text{photon}}Ephoton​ is the energy of the photon,
• $\varphi$ is the work function of the metal.

Example Metals:

1. Sodium (Na): The work function of sodium is approximately 2.28 eV.

   • If the photon energy is 5.1 eV, the kinetic energy of the emitted electrons will be:
   $$K.E.=5.1\text{eV}-2.28\text{eV}=2.82\text{eV}$$

2. Copper (Cu): The work function of copper is about 4.7 eV.

   • For 5.1 eV photons, the kinetic energy of the emitted electrons will be:
   $$K.E.=5.1\text{eV}-4.7\text{eV}=0.4\text{eV}$$

Conclusion:

Electrons emitted from sodium will have higher kinetic energy (2.82 eV) compared to electrons emitted from copper (0.4 eV) because sodium has a lower work function, allowing more energy to be available for the kinetic energy of the emitted electrons when photons with 5.1 eV strike the metal.