The Photoelectric Equation
Maximum electron energy, photon energy, and the work function
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According to Einstein:
wo = work function - work to pull away electron (different for each metal) hf = Energy of light used
Emax = Energy of photoelectron (Max KE given to electron)
Electronvolt
- very small energy unit:
Einstein uses y = mx + b to get his equation!
2. Threshold frequency - minimum frequency needed to expel electrons
Explained by Einstein
Typical plot of Frequency vs. Emax (Maximum KE of photoelectron)
Frequency
Threshold frequency of: Metal A?
fo = 1.0 X 1014 Hz
Metal B?
Frequency
fo = 2.5 X 1014 Hz
Metal C?
Frequency
fo = 3.75 x 1014 Hz
Which metal has the
Frequency
Work Function - energy needed to pull away electron from atom.
h = Planck's Constant p.1 Reference
Ex 1) If a metal would only emit electrons when exposed to high frequency light what does that tell you about its work function?
Work function must be high
Ex)
If the work function (Wo) of particular metal = 5.0 x 10-19
J Find the threshold frequency (fo) ( h = 6.63 x 10-34 Js ) Wo = hfo fo = w/h = (5 x 10-19 J/(6.63 x 10-34 Js)
fo = 7.5 x 1014 Hz
Since KEmax= hf - wo
Then …
(Use equation if given only frequencies)
PHOTON BY PHOTON DEVELOPMENT
Ref: P.G. Hewitt, Conceptual Physics, 9th ed.©2002 Pearson Education
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Explore: Photon Energy and Frequency
Ephoton = hf — the higher the frequency, the more energy each photon carries.
Slide the frequency and read the photon energy in joules and electron-volts.
Compare the photon energy of red light (about 4.3 × 1014 Hz) with ultraviolet (about 1.0 × 1015 Hz). Which is more likely to eject electrons from a metal?
Red: about 1.8 eV. UV: about 4.1 eV. The ultraviolet photons carry more energy, so they are more likely to exceed a metal’s work function.
Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. In Emax = hf − W₀, what does W₀ (the work function) represent?
2. Light with photon energy 5.0 eV hits a metal with work function 2.0 eV. What is the maximum KE of the photoelectrons?
3. A metal has a work function of 5.0 × 10⁻¹⁹ J. What is its threshold frequency? (h = 6.63 × 10⁻³⁴ J·s)
4. Metals A, B and C have threshold frequencies 1.0, 2.5 and 3.75 × 10¹⁴ Hz. Which has the greatest work function?
5. Photons of 1.5 eV hit a metal with a 2.0 eV work function. Making the light much brighter will…
Graphing Photoelectric Data
Students measured the maximum kinetic energy of electrons ejected from a metal by light of different frequencies. Their data are shown in Table 1.
Table 1: Photoelectric Data
| Frequency (× 1014 Hz) | 6.0 | 8.0 | 10.0 | 12.0 |
|---|---|---|---|---|
| KEmax (eV) | 0.20 | 1.03 | 1.86 | 2.69 |
What does the slope of a graph of KEmax versus frequency represent?
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. Which graph best represents KEmax versus frequency?
C2. Substitute values from Table 1 into a mathematical representation that can be used to determine the slope of the KEmax versus frequency graph, using the first and last data points. Then calculate the slope.
C3. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using the data in Table 1.
C4. Using the slope h = 4.15 × 10−15 eV·s and the first data point in Table 1, determine the work function of the metal.
C5. The experiment is repeated with a different metal that has a larger work function. How does its graph compare?
C6. Identify the evidence in Table 1 that KEmax depends linearly on frequency, and describe how a graph of the data could be used to find the threshold frequency.