Photoelectric effect — KCSE Physics

In the photoelectric effect, certain key terms are essential to grasp:

• Threshold Frequency (f₀): This is the minimum frequency of incident light required to eject electrons from a metal surface. If the frequency is below this threshold, no electrons will be emitted, regardless of light intensity.

• Work Function (Φ): This is the minimum energy needed to remove an electron from the surface of the metal. It is usually measured in electron volts (eV). The work function is related to the threshold frequency by the equation:

  [ \Phi = h f_0 ]

  where ( h ) is Planck's constant (6.63 x 10^-34 J·s).

• Electron Volt (eV): This is a unit of energy equal to the amount of kinetic energy gained by an electron when it is accelerated through a potential difference of one volt. 1 eV = 1.6 x 10^-19 Joules.

To find the energy of a photon, use the formula:

[ E = hf ]

where ( E ) is the energy, ( h ) is Planck's constant, and ( f ) is the frequency of the light.

The photoelectric effect occurs when light shines on a metal surface, causing the emission of electrons. Einstein's equation, E = hf - W, explains this phenomenon:

• E is the kinetic energy of the emitted electrons.
• h is Planck's constant (6.63 x 10^-34 Js).
• f is the frequency of the incident light.
• W is the work function of the metal, the minimum energy needed to release an electron.

When light of sufficient frequency strikes the metal, it transfers energy to the electrons. If the energy exceeds the work function, electrons are emitted with kinetic energy equal to the difference between the photon energy and the work function.

Applications of the photoelectric effect include:

• Photoelectric cells in solar panels convert sunlight into electricity.
• Photodetectors in cameras that adjust exposure based on light levels.
• Electron microscopes that utilize emitted electrons for high-resolution imaging.

The photoelectric effect demonstrates how light can eject electrons from a material. To solve problems related to this effect, you need to calculate:

1. Photon Energy (E): Use the formula:
   [ E = hf ]
   where ( h ) is Planck's constant (6.63 × 10⁻³⁴ J·s) and ( f ) is the frequency of light.

2. Maximum Kinetic Energy (K.E.): This is given by:
   [ K.E. = E - \phi ]
   where ( \phi ) is the work function of the material.

3. Stopping Potential (V_s): It is calculated using:
   [ V_s = \frac{K.E.}{e} ]
   where ( e ) is the charge of an electron (1.6 × 10⁻¹⁹ C).

4. Velocity of Photoelectrons (v): Use the formula:
   [ v = \sqrt{\frac{2K.E.}{m}} ]
   where ( m ) is the mass of an electron (9.11 × 10⁻³¹ kg).

By applying these formulas, you can solve various problems related to the photoelectric effect effectively.