The photoelectric effect

1. Definition and Key Concepts

• The photoelectric effect occurs when light energy ejects electrons from a metal surface.
• Light energy is carried in small packets called photons.
• A photon has a specific energy $(E)$ that depends on its frequency $(f):$

Where: $E = hf$

• $h =$ Planck's constant $(6.63 × 10⁻³⁴ J·s).$
• $f =$ Frequency of the incident light $(Hz).$

2. Conditions for Electron Emission

1. Threshold Frequency $(f_0)$

• Each metal has a minimum frequency below which no electrons are emitted, regardless of intensity.
• If $f < f_0 →$ No photoelectrons emitted.
• If $f = f_0 →$ Electrons are emitted but have zero kinetic energy.
• If $f > f_0 →$ Electrons are emitted with kinetic energy.

2. Work Function $(W_0)$

• The minimum energy required to eject an electron from a metal surface.
• Related to threshold frequency: $W_0 = h f_0$

3. Energy of Photoelectrons

• The total energy of the photon is split into: $E = W_0 + K_e$

• Work function $(W_0):$ Energy needed to remove the electron.

• Kinetic energy $(K_e):$ The remaining energy of the ejected electron. $hf = h f_0 + \frac{1}{2} m v^2$

Where:

• $m =$ Mass of electron $(9.11 × 10⁻³¹ kg).$
• $v =$ Velocity of electron $(m/s).$

4. Changing the Frequency and Intensity of Light

1. Increasing Frequency $(f)$:

• Increases the kinetic energy of emitted electrons.
• Same number of electrons are emitted per second (if intensity is constant).

2. Increasing Intensity (Brightness):

• More photons strike the surface per second.
• More electrons are emitted.
• No effect on electron kinetic energy (if frequency remains unchanged).

5. Applications of the Photoelectric Effect

• Solar panels: Convert sunlight into electricity.
• Photoelectric diodes: Used in smoke detectors, cameras, and automatic doors.
• Light sensors: Used in remote controls and night-vision devices.

6. Key Takeaways

• Electrons are only ejected if the light frequency is above the threshold frequency.
• Increasing intensity only increases the number of ejected electrons, not their energy.
• Photoelectric effect supports the idea that light behaves as a particle (photon).