Rearranging hf = W + KEmax gives KEmax = hf − W. Plotted with KEmax on the vertical axis and f on the horizontal axis, this is a straight line with gradient h.
This lesson is part of SPM Physics. It builds on explaining the photoelectric effect.
What does each part of the graph mean?
| Feature of the line | What it gives | Why |
|---|---|---|
| Gradient | Planck’s constant h | KEmax = hf − W has the form y = mx + c |
| Intercept on the f-axis | Threshold frequency f₀ | KEmax = 0 when hf₀ = W |
| Extended intercept on the KE-axis | −W | At f = 0, KEmax = −W |
Worked example: reading two points
An original graph shows a straight line starting on the frequency axis at 5.0 × 10¹⁴ Hz. The line passes through the point f = 1.0 × 10¹⁵ Hz, KEmax = 3.3 × 10⁻¹⁹ J.
Threshold frequency: f₀ = 5.0 × 10¹⁴ Hz.
Gradient: the rise is 3.3 × 10⁻¹⁹ J over a run of 1.0 × 10¹⁵ − 5.0 × 10¹⁴ = 5.0 × 10¹⁴ Hz. h = 3.3 × 10⁻¹⁹ ÷ 5.0 × 10¹⁴ = 6.6 × 10⁻³⁴ J s.
Work function: W = hf₀ = 6.6 × 10⁻³⁴ × 5.0 × 10¹⁴ = 3.3 × 10⁻¹⁹ J.
The mistake that costs marks
The slip is to read the gradient as the work function. Another slip is to divide the KE of one point by its frequency and call that the gradient.
| Step | Wrong | Right |
|---|---|---|
| Gradient | 3.3 × 10⁻¹⁹ ÷ 1.0 × 10¹⁵ = 3.3 × 10⁻³⁴ | Use the rise and run between two points on the line |
| Work function | Gradient | hf₀, or the magnitude of the KE-axis intercept |
Dividing by the whole frequency ignores that the line does not start at the origin. Always take the run from two points on the line itself.
How do two metals compare?
Two metals obey the same equation with the same h, so their lines have the same gradient. They differ only in W, so the lines are parallel.
The metal with the larger work function has the larger threshold frequency, and its line sits further to the right. Changing the intensity of the light does not move or tilt the line, since each point already gives the maximum kinetic energy.
Check yourself
A line on a KEmax against f graph passes through (6.0 × 10¹⁴ Hz, 0) and (1.0 × 10¹⁵ Hz, 2.65 × 10⁻¹⁹ J). Find h and W.
Answer
Gradient: 2.65 × 10⁻¹⁹ ÷ (1.0 × 10¹⁵ − 6.0 × 10¹⁴) = 2.65 × 10⁻¹⁹ ÷ 4.0 × 10¹⁴ = 6.6 × 10⁻³⁴ J s.
W = hf₀ = 6.6 × 10⁻³⁴ × 6.0 × 10¹⁴ = 4.0 × 10⁻¹⁹ J.
What to study next
Put the graph together with the physical explanation in distinguishing photon explanations from classical expectations. Then test yourself with the quantum physics practice set.
For general graph habits, read reading physics graphs without confusing slope and area. If you want a teacher to go through graphs with you, see online one-to-one Physics tuition.