Optical Phenomena and Properties of Matter Revision Notes for Grade 12 NSC Matric Physical Sciences

The Photoelectric Effect

Introduction and historical background

The photoelectric effect was one of the most important discoveries in physics that helped establish the quantum nature of light. Around the turn of the twentieth century, physicists including Heinrich Hertz, Philipp Lenard, and others observed that when light was shone onto a metal plate, electrons were emitted by the metal.

In 1887, Heinrich Hertz noticed that ultraviolet light incident on a metal plate could cause sparks. This was puzzling because metals are good conductors of electricity, so electrons should be able to move easily. Scientists expected that different metals would require different minimum frequencies of light to release electrons.

The initial expectation was that electrons would be emitted for any frequency of light after a delay, during which the electrons absorbed sufficient energy to escape from the metal surface. Scientists thought that higher intensity light would lead to shorter delays and higher electron velocities, based on the idea that light was a wave continuously delivering energy to the electrons.

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However, the observations did not match these expectations, creating a paradox that classical physics could not explain. This contradiction between wave theory predictions and experimental observations became one of the key pieces of evidence for the quantum nature of light.

Definition of the photoelectric effect

The photoelectric effect is the process whereby an electron is emitted by a substance when light shines on it.

This phenomenon occurs when electromagnetic radiation strikes a metal surface containing a "sea of electrons." When the incoming radiation has sufficient energy, it knocks electrons out of the metal surface.

Key observations that puzzled scientists

Philipp Lenard made a crucial discovery in 1902: the maximum velocity of electrons ejected by ultraviolet light was entirely independent of the intensity of light.

Additionally, different metals required different minimum frequencies of light to eject electrons, regardless of the light's intensity.

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The experimental demonstration shows that red light incident on a zinc plate causes no change in the electroscope, even if the intensity is increased. However, ultraviolet light of low intensity causes the electroscope leaf to collapse.

Einstein's quantum explanation

Albert Einstein proposed that light is made up of packets of energy called quanta (now called photons).

Work function concept

The work function is the minimum energy needed to knock an electron out of a metal. It is represented by the symbol W₀.

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$W_0 = hf_0$

Where:

$W_0$ = work function (J)
$h$ = Planck's constant
$f_0$ = threshold frequency (Hz)

The photoelectric equation

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$E = W_0 + E_{k_{max}}$

$E_{k_{max}} = hf - W_0$

Where:

$E$ = photon energy = $hf$
$W_0$ = work function
$E_{k_{max}}$ = maximum kinetic energy

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Below the threshold frequency ( $f_0$ ), no emission occurs regardless of intensity.

Worked example 1: Maximum kinetic energy calculation

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Question: Ultraviolet radiation with wavelength 250 nm is incident on silver foil ( $W_0 = 6.9 \times 10^{-19}$ J).

$E_{k_{max}} = \frac{hc}{\lambda} - W_0$

$E_{k_{max}} = 7.96 \times 10^{-19} - 6.9 \times 10^{-19}$

$E_{k_{max}} = 1.06 \times 10^{-19} \text{ J}$

Worked example 2: Threshold frequency analysis

lightbulbExample

$E_{photon} = hf = 7.96 \times 10^{-19} \text{ J}$

$W_{0_{gold}} = 8.2 \times 10^{-19} \text{ J}$

$E_{photons} < W_{0_{gold}}$

Worked example 3: NSC exam-style question

lightbulbExample

Using $E = W_0 + K$ :

$hf = W_0 + K$ $6.03 \times 10^{-19} = 3.5 \times 10^{-19} + K$ $K = 2.53 \times 10^{-19} \text{ J}$

Exam tips and common traps

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Make sure you can rearrange:

$E = hf = W_0 + E_{k_{max}}$

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Key Points to Remember:

$E_{k_{max}} = hf - W_0$
Threshold frequency = $f_0$
Work function = $W_0$
Photon energy = $hf$

Optical Phenomena and Properties of Matter (Grade 12 NSC Matric Physical Sciences): Revision Notes

The Photoelectric Effect

Introduction and historical background

Definition of the photoelectric effect

Key observations that puzzled scientists

Einstein's quantum explanation

Work function concept

The photoelectric equation

Worked example 1: Maximum kinetic energy calculation

Worked example 2: Threshold frequency analysis

Worked example 3: NSC exam-style question

Exam tips and common traps

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