Photoelectric Effect (Copy)

Definition and Description

• The photoelectric effect is the emission of photoelectrons (electrons) from the surface of a metal when electromagnetic radiation (usually UV or visible light) of sufficient frequency is incident on it.
• Demonstrates the particle nature of light — energy is carried in photons, not as a continuous wave.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

1. Key Terms

• Photoelectrons: Electrons emitted from a metal surface when struck by photons.
• Threshold frequency (f₀): The minimum frequency of incident radiation required to release photoelectrons from the surface of a given metal.
• Threshold wavelength (λ₀): The maximum wavelength that can cause photoelectric emission for a given metal.

Relationship:

• f0=Φhf_0 = dfrac{Φ}{h}
• λ0=cf0=hcΦλ_0 = dfrac{c}{f_0} = dfrac{hc}{Φ}

Where:

• ΦΦ = work function energy (J)
• hh = Planck’s constant
• cc = speed of light

2. Explanation of the Photoelectric Effect

• A photon strikes the metal surface.
• If the photon’s energy E=hfE = hf is greater than or equal to the work function ΦΦ, it can eject an electron from the surface.
• Excess energy is transferred to the photoelectron as kinetic energy.

3. The Photoelectric Equation

hf=Φ+12mvmax2hf = Φ + dfrac{1}{2}mv_{text{max}}^2

Where:

• hfhf = energy of the incident photon
• ΦΦ = work function of the metal (minimum energy needed to release the electron)
• 12mvmax2dfrac{1}{2}mv_{text{max}}^2 = maximum kinetic energy of the emitted electron
• vmaxv_{text{max}} = maximum velocity of photoelectron

If hf<Φhf < Φ, no photoemission occurs, regardless of the intensity.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

4. Graphical Interpretation

Graph of 12mv2dfrac{1}{2}mv^2 vs Frequency ff:

• Gradient = hh
• Y-intercept = −Φ-Φ
• X-intercept = f0f_0

5. Effect of Light Intensity

• Increasing intensity = more photons per second → more photoelectrons emitted → greater photoelectric current (if f>f0f > f_0).
• However, intensity has no effect on kinetic energy of emitted photoelectrons.
  • K.E. depends only on frequency, not intensity.
• So:
  • Photoelectric current ∝ Intensity
  • Max kinetic energy ∝ Frequency, not intensity

6. Key Observations from Experiments

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

7. Work Function (Φ)

• The work function is the minimum energy required to release an electron from the surface of a metal.
• Units: Joules (J) or electronvolts (eV)

Conversion:

• 1 eV=1.60×10−19 J1 , text{eV} = 1.60 times 10^{-19} , text{J}

Example:

If a metal has a work function of 3.0 eV:

Φ=3.0×1.60×10−19=4.8×10−19 JΦ = 3.0 times 1.60 times 10^{-19} = 4.8 times 10^{-19} , text{J}

8. Energy Level Diagram (Visual Concept)

• Photon of energy hfhf hits metal.
• If hf>Φhf > Φ, electron escapes with K.E. = hf−Φhf – Φ
• If hf=Φhf = Φ, electron escapes with zero K.E.
• If hf<Φhf < Φ, no emission occurs.