Physics 9702 (A Level) Study Notes: 22.2 Photoelectric Effect
Hello future quantum physicist! This chapter is where classical physics breaks down and we dive into the fascinating world of quantum mechanics. The Photoelectric Effect is the most crucial experimental evidence that light sometimes behaves like a particle (a photon), not just a wave. Don't worry if this seems tricky at first—we’ll break it down step-by-step!
The core idea: The photoelectric effect is about how light can knock electrons out of a metal surface.
1. Understanding the Phenomenon (The Basics)
What is the Photoelectric Effect?
The photoelectric effect occurs when photoelectrons (electrons emitted by light) are ejected from a metal surface after it is illuminated by electromagnetic radiation (light).
When scientists first studied this effect using classical wave theory, they ran into some massive problems. Classical physics predicted three things that turned out to be wrong:
- Classical Error 1: Brighter light (higher intensity) should mean more energy, so it should eject electrons with higher kinetic energy. (WRONG)
- Classical Error 2: Any frequency of light should eventually cause emission if the intensity is high enough, given time for the energy to build up. (WRONG)
- Classical Error 3: There should be a measurable time delay between the light striking the surface and the electron being ejected. (WRONG)
The failure of classical theory to explain these observations led to the quantum revolution, spearheaded by Einstein using Planck's idea of quantization.
Key Takeaway:
The photoelectric effect is the emission of electrons from a metal surface when light shines on it. Classical wave theory failed miserably to explain it, requiring a new approach.
2. Key Quantum Concepts (The Vocabulary)
To understand the explanation, we must first accept that light energy comes in discrete packets called photons (as learned in 22.1). The energy \(E\) of one photon is directly proportional to its frequency \(f\):
$$E = hf$$
where \(h\) is the Planck constant ($6.63 \times 10^{-34} \text{ J s}$).
a) Work Function (\(\Phi\))
The metal surface holds onto its electrons. To escape, an electron needs a certain amount of minimum energy.
Definition: The Work Function (\(\Phi\), pronounced 'Phi') is the minimum energy required to remove a single electron from the surface of a specific metal.
Analogy: Think of the work function as the "entrance fee" an electron must pay to leave the metal club and enter the outside world.
b) Threshold Frequency (\(f_0\))
Since energy is tied to frequency (\(E=hf\)), there must be a minimum frequency required for the photon to have enough energy to pay the Work Function fee.
Definition: The Threshold Frequency (\(f_0\)) is the minimum frequency of incident radiation below which no photoelectrons are emitted, no matter how intense the light source is.
If \(f = f_0\), the photon energy \(hf_0\) is just enough to liberate the electron, leaving it with zero kinetic energy. Therefore:
$$\Phi = hf_0$$
c) Threshold Wavelength (\(\lambda_0\))
If we talk about frequency, we must also talk about wavelength. Since $c = f\lambda$, if the frequency is minimum (\(f_0\)), the wavelength must be maximum (\(\lambda_0\)).
Definition: The Threshold Wavelength (\(\lambda_0\)) is the maximum wavelength of incident radiation that can still cause photoelectric emission.
If you shine light with a wavelength longer than \(\lambda_0\), the photons do not have enough energy, and no emission occurs.
Quick Review Box: Threshold Conditions
For emission to occur, the incident photon energy ($E = hf$) must be greater than the Work Function ($\Phi$).
Condition for emission: \(hf > \Phi\) or \(f > f_0\) or \(\lambda < \lambda_0\) (Notice the inequality flip for wavelength!)
3. Einstein's Photoelectric Equation
Einstein successfully explained the experimental observations using the concept of discrete photons and the conservation of energy. This is sometimes called the Photon Model.
Step-by-Step Energy Transfer:
- A photon of energy \(hf\) strikes the metal surface.
- The photon's energy is completely absorbed by a single electron in a one-to-one interaction.
- A minimum portion of that energy, \(\Phi\), is used to overcome the binding forces (the Work Function).
- The remaining energy is converted entirely into the kinetic energy ($E_{K}$) of the emitted photoelectron.
The electron that is right at the surface requires only the minimum energy \(\Phi\) to escape. Therefore, it leaves with the maximum kinetic energy (\(E_{K \text{ max}}\)).
The Photoelectric Equation (Energy Conservation)
$$ \text{Photon Energy} = \text{Energy to Escape} + \text{Remaining Kinetic Energy} $$ $$ hf = \Phi + E_{K \text{ max}} $$
Since the maximum kinetic energy is defined as $E_{K \text{ max}} = \frac{1}{2}mv^2_{\text{max}}$, the full equation used in 9702 syllabus is:
$$\mathbf{hf = \Phi + \frac{1}{2}mv^2_{\mathbf{max}}}$$
Where:
\(h\) = Planck constant
\(f\) = frequency of incident radiation
\(\Phi\) = Work Function (minimum energy to escape)
\(m\) = mass of the electron
\(v_{\text{max}}\) = maximum speed of the photoelectron
We can rearrange this equation to find the maximum kinetic energy:
$$E_{K \text{ max}} = hf - \Phi$$
Did you know? (Units Check)
In quantum physics, energies are often very small, so we use the electronvolt (eV) instead of Joules (J).
1 eV is the kinetic energy gained by an electron when accelerated through a potential difference of 1 Volt.
Recall: \(1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}\).
Key Takeaway:
The photoelectric equation $hf = \Phi + E_{K \text{ max}}$ is an application of the conservation of energy, showing that all photon energy is split between freeing the electron and giving it kinetic energy.
4. Explaining Experimental Observations (22.2.5)
The equation $E_{K \text{ max}} = hf - \Phi$ allows us to explain the two counter-intuitive observations regarding intensity and frequency.
a) The Effect of Frequency (Explains the Threshold)
If you increase the frequency (\(f\)), you increase the energy of each individual photon (\(hf\)).
Since \(\Phi\) is constant for a given metal, increasing \(hf\) means the maximum kinetic energy ($E_{K \text{ max}}$) increases linearly.
If \(f\) is too low (less than \(f_0\)), \(hf\) is less than \(\Phi\). The electron cannot escape, and $E_{K \text{ max}}$ remains zero. This perfectly explains why there is a threshold frequency.
b) The Effect of Intensity (The Crucial Distinction)
This is where students often struggle, but remember the photon model: Intensity is about QUANTITY; Frequency is about QUALITY.
i) Maximum Kinetic Energy is Independent of Intensity
1. Intensity: Intensity is the rate of energy flow per unit area, which in the quantum model means the number of photons hitting the surface per second.
2. Kinetic Energy: Maximum kinetic energy depends only on the energy of a single photon, $E_{K \text{ max}} = hf - \Phi$. It does not depend on how many photons there are.
3. The Result: If you use a brighter light (increase intensity) but keep the frequency the same, you are sending more photons of the same energy. Therefore, you knock out more electrons, but *each* electron leaves with the same maximum kinetic energy.
ii) Photoelectric Current is Proportional to Intensity
1. Photoelectric Current: This is the flow rate of the ejected electrons.
2. Proportionality: Since the process is a one-to-one interaction (one photon ejects one electron):
Higher Intensity \(\rightarrow\) More Photons per second \(\rightarrow\) More Electrons ejected per second \(\rightarrow\) Higher Current.
Therefore, the photoelectric current is directly proportional to the intensity of the incident radiation (provided \(f > f_0\)).
Common Mistake to Avoid:
Do not confuse Intensity and Frequency!
If asked to increase the energy of the photoelectrons, you must increase the frequency.
If asked to increase the number of photoelectrons (the current), you must increase the intensity.
Key Takeaway:
Frequency controls the energy of individual electrons ($E_{K \text{ max}}$). Intensity controls the number of electrons ejected (the current).