Grade 11

Advanced

7 min

Lesson 9 of 12

The Photoelectric Effect

Not Started

The phenomenon that challenged classical wave theory and introduced the concept of light as particles.

Imagine a locked door that won't budge no matter how many people push on it at once, yet opens instantly for a single person holding the right key. In the world of physics, light behaves exactly like this—and it completely broke our understanding of the universe.

Learning Objectives

1.Describe the experimental observation of electron emission from metal surfaces
2.Identify why classical wave theory failed to explain the threshold frequency
3.Define the work function and threshold frequency of a metal

The Observation: Light as a Hammer

In 1887, Heinrich Hertz noticed something strange: sparks jumped more easily between electrodes when they were illuminated by ultraviolet light. This is the Photoelectric Effect: the emission of electrons (called photoelectrons) from a material's surface when light shines on it. According to classical physics, light was a continuous wave. If you increased the intensity (brightness) of the light, you were pumping more energy into the metal, which should eventually shake electrons loose regardless of the light's color. But experiments showed something impossible: for some metals, even the brightest red light did nothing, while the dimmest blue light caused immediate emission.

Quick Check

In the photoelectric effect, what are the ejected particles called?

They are electrons emitted due to light (photons).

Answer

Photoelectrons

The Classical Failure

Classical wave theory predicted that if you waited long enough, any light should eventually eject an electron. However, scientists discovered a threshold frequency ( $f_0$ ). This is the minimum frequency of light required to eject an electron from a specific metal. If the light's frequency is below $f_0$ , no electrons are emitted, no matter how intense the light is or how long you wait. This suggested that light isn't just a continuous wave, but arrives in discrete "packets" of energy. This discovery was the first major crack in the foundation of classical physics.

A specific metal has a threshold frequency of $f_0 = 5.0 \times 10^{14} \text{ Hz}$ . 1. Light A has a frequency of $4.5 \times 10^{14} \text{ Hz}$ . 2. Light B has a frequency of $6.0 \times 10^{14} \text{ Hz}$ .

Result: Only Light B will eject electrons because its frequency is higher than the threshold ( $f_B > f_0$ ). Light A will never eject electrons, regardless of its brightness.

Einstein’s Solution: The Work Function

Albert Einstein solved the mystery by proposing that light consists of particles called photons. Each photon carries a specific amount of energy defined by

E = hf

, where

h

is Planck’s constant (

6.626 \times 10^{-34} \text{ J}\cdot\text{s}

). To escape the metal, an electron must overcome a binding energy known as the Work Function (

\Phi

). Think of the work function as a "toll" the electron must pay to leave the surface. The threshold frequency is simply the frequency where the photon energy exactly equals the work function:

\Phi = hf_0

Calculate the energy of a single photon of violet light with a frequency of $7.5 \times 10^{14} \text{ Hz}$ . 1. Use the formula $E = hf$ . 2. Substitute values: $E = (6.626 \times 10^{-34} \text{ J}\cdot\text{s})(7.5 \times 10^{14} \text{ Hz})$ . 3. $E \approx 4.97 \times 10^{-19} \text{ J}$ .

Quick Check

What happens to the excess energy if a photon has more energy than the work function?

Energy must be conserved; if the 'toll' is paid, the rest is used for speed.

Answer

It becomes the kinetic energy of the ejected electron.

The Conservation of Energy

Einstein’s Photoelectric Equation is a statement of energy conservation:

hf = \Phi + K_{max}

Here,

hf

is the incoming photon energy,

\Phi

is the energy required to escape, and

K_{max}

is the maximum kinetic energy of the ejected electron. If the photon has more energy than the work function, the "change" is given to the electron as speed. Increasing the intensity (brightness) of light increases the number of photons (and thus the number of electrons), but it does not increase the speed of individual electrons. Only increasing the frequency increases their speed.

A metal has a work function $\Phi = 2.3 \text{ eV}$ . If light with frequency $f = 8.0 \times 10^{14} \text{ Hz}$ hits the metal, find $K_{max}$ in Joules. (Note: $1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$ ). 1. Convert $\Phi$ to Joules: $2.3 \times 1.6 \times 10^{-19} = 3.68 \times 10^{-19} \text{ J}$ . 2. Calculate photon energy: $E = hf = (6.626 \times 10^{-34})(8.0 \times 10^{14}) = 5.30 \times 10^{-19} \text{ J}$ . 3. Solve for $K_{max}$ : $K_{max} = hf - \Phi = 5.30 \times 10^{-19} - 3.68 \times 10^{-19} = 1.62 \times 10^{-19} \text{ J}$ .

Key Takeaways

1The photoelectric effect proves light behaves as discrete particles called photons.
2The Work Function ( $\Phi$ ) is the minimum energy required to liberate an electron from a metal surface.
3The energy of a photon is directly proportional to its frequency ( $E = hf$ ).
4Intensity affects the number of electrons emitted, while frequency affects their maximum kinetic energy.

Quick Check

Multiple Choice

What happens if you increase the intensity of light that is below the threshold frequency?

Multiple Choice

Which variable determines the maximum kinetic energy of photoelectrons?

True/False

The photoelectric effect can be fully explained using classical wave theory.

What's Next?

Review Tomorrow

In 24 hours, try to write down Einstein's photoelectric equation from memory and explain what each term represents.

Practice Activity

Research why different metals (like Cesium vs. Platinum) have different work functions and how this is used in night-vision goggles.

Browse

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The Photoelectric Effect

Learning Objectives

The Observation: Light as a Hammer

The Classical Failure

Einstein’s Solution: The Work Function

The Conservation of Energy

Key Takeaways

Quick Check

What's Next?

The Photoelectric Effect

Learning Objectives

The Observation: Light as a Hammer

The Classical Failure

Einstein’s Solution: The Work Function

The Conservation of Energy

Key Takeaways

Quick Check

What's Next?