22.2.2Quantum and nuclear physics (A Level)
Threshold Frequency
5 min read 9 parts Lesson 7 of 23 1 quiz
Lesson summary
22.2.2 Threshold Frequency — AS PHYSICS 9702 notes: Define threshold frequency and wavelength, relate them to the work function and use the graph of maximum kinetic energy against frequency.Threshold frequency = the minimum frequency of incident radiation needed to remove a photo…
- Below threshold
- At threshold
- Above threshold
- Property of the metal
- Threshold wavelength
- Condition for emission
Section 1 of 9Threshold frequency
Threshold frequency
Threshold frequency the minimum frequency of incident radiation needed to remove a photoelectron from the surface of a metal.
Below threshold
- For f < f0 no electrons are emitted, whatever the intensity.
At threshold
- At f = f0 the photon has just enough energy and the electron leaves with no kinetic energy.
Above threshold
- For f > f0 the extra energy becomes kinetic energy of the photoelectron.
Property of the metal
- The threshold varies from metal to metal and depends on the surface condition.
- Contamination or oxide layers change the effective work function.
Section 2 of 9Threshold wavelength
Threshold wavelength
Threshold wavelength the longest wavelength of incident radiation that can remove a photoelectron from the surface of a metal.
Relation
- λ0 = c/f0.
Condition for emission
- Emission needs f > f0, which means λ < λ0.
- A lower frequency means a longer wavelength, so the inequality reverses.
Section 3 of 9Values for different metals
| Metal | Threshold frequency f0 / Hz | Threshold wavelength λ0 / nm |
|---|---|---|
| Sodium | 4.40 × 1014 | 682 |
| Potassium | 5.56 × 1014 | 540 |
| Zinc | 1.02 × 1015 | 294 |
| Iron | 1.04 × 1015 | 289 |
| Copper | 1.13 × 1015 | 266 |
| Gold | 1.23 × 1015 | 244 |
Alkali metals
- Sodium and potassium have thresholds in the visible region because surface electrons are only weakly attracted to the positive ions.
Transition metals
- Iron and similar metals have thresholds in the ultraviolet because the attraction is much stronger.
Section 4 of 9Link with the work function
Link with the work function
Work function at threshold
- Φ = hf0.
Rearranged
- Rearranged f0 = Φ/h and λ0 = hc/Φ.
Small Φ
- Metals with small work functions have low threshold frequency and long threshold wavelength.
Large Φ
- Metals with large work functions need ultraviolet radiation.
Section 5 of 9Graph of maximum kinetic energy against frequency
Shape
- A straight line with positive gradient, with points only for f above f0.
Equation
- Ek max = hf − Φ, compared with y = mx + c.
Gradient
- The gradient equals the Planck constant h and is the same for every metal.
Frequency intercept
- The line meets the frequency axis at the threshold frequency f0.
Energy intercept
- Extending the line back to f = 0 gives −Φ on the vertical axis.
Different metals
- They give parallel lines shifted along the frequency axis.
Finding h
- Measure Ek max from the stopping potential for several frequencies, plot the graph and find the gradient.
Section 6 of 9Using the threshold
Will emission occur
- Compare frequencies or wavelengthsf > f0 or λ < λ0.
Maximum kinetic energy
- Ek max = h(f − f0) from Einstein's equation.
Intensity
- It fixes only how many electrons are emitted, not whether emission occurs.
Section 7 of 9More from the specification
Energy transferred
- W = V Q, in joules.What the symbols mean: E or W = energy transferred (J) · Q = charge (C) · V = potential difference (V) · I = current (A) · t = time (s)
Current
- Flow of electrons in a circuit.
Photoelectric current
- The charge per second carried by photoelectrons, proportional to the number emitted per second.
E
E hf = Φ + 12 mv2max
What the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10−34 J s) · f = frequency (Hz)
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Threshold frequency | The minimum frequency of electromagnetic radiation required to remove a photoelectron from the surface of a metal. |
| Threshold wavelength | The longest wavelength of electromagnetic radiation that can remove a photoelectron from the surface of a metal. |
| Work function (Φ) | The minimum energy needed to release an electron from the surface of a metal, Φ = hf0. |
| Maximum kinetic energy | The greatest kinetic energy of emitted photoelectrons, Ek max = hf − Φ. |
| Planck constant | The gradient of the Ek max against f graph, 6.63 × 10−34 J s. |
Section 9 of 9Exam technique
1
Writing that emission occurs when λ > λ0 — emission needs a wavelength shorter than the threshold wavelength.
2
Thinking intense low-frequency light can eventually cause emission — below the threshold frequency there is no emission at any intensity.
3
Drawing the Ek max against f graph through the origin — it crosses the f-axis at f0.
4
Assuming different metals give lines of different gradient — the gradient is always h.
5
Mixing up the intercepts — the vertical intercept is −Φ and the horizontal intercept is f0.