The Photoelectric Effect
The electronvolt, threshold frequency, work function, stopping potential, and Einstein's photoelectric equation.
Spec Points Covered
- Define the electronvoltA unit of energyThe capacity to do work. Measured in joules (J). equal to the energyThe capacity to do work. Measured in joules (J). gained by one electron accelerated through a potential difference of 1 V. 1 eV = 1.6 x 10⁻¹⁹ J. and convert between eV and joules.
- Describe the photoelectric effectThe emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). is incident on it. and explain why it provides evidence for the particle nature of light.
- Define threshold frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz).The minimum frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). of incident radiation required to cause photoelectric emission from a particular metal surface., threshold wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m). and work functionThe minimum energyThe capacity to do work. Measured in joules (J). required to liberate an electron from the surface of a metal..
- Apply the photoelectric equation: $hf = \phi + E_{k}(max)$.
- Explain the significance of stopping potentialThe minimum potential difference required to stop the most energetic photoelectrons emitted in the photoelectric effect. and use E_k(max) = eV_s.
- Explain why increasing intensityThe powerThe rate of energy transfer. Measured in watts (W). transmitted per unit area perpendicular to the wave direction. Measured in W m⁻². Proportional to amplitude squared. increases photoelectric currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). but not maximum kinetic energyThe energy an object possesses due to its motion..
- Interpret graphs of E_k(max) against frequency to find work functionThe minimum energy required to liberate an electron from the surface of a metal., threshold frequencyThe minimum frequency of incident radiation required to cause photoelectric emission from a particular metal surface. and Planck's constant.
Notes
01
The electronvolt is a convenient energy unit for quantum physics
Electronvolt
3.2.2.1
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02
The photoelectric effect shows light behaves as particles
Photoelectric effect
3.2.2.1
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03
Threshold frequency and work function define when emission starts
Threshold frequency
3.2.2.1
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04
The photoelectric equation: hf = φ + E_k(max)
$hf = \phi + E_{k(\max)}$
3.2.2.1
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05
Stopping potential measures maximum kinetic energy
Stopping potential
3.2.2.1
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06
Intensity affects photoelectric current, not kinetic energy
3.2.2.1
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07
The E_k vs f graph gives work function, threshold frequency and Planck's constant
3.2.2.1
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On Data Sheet
Not on Data Sheet
Electronvolt conversion
$$1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}$$
- Where:
- $eV$ = electronvolt
- $J$ = joule
eV → J: multiply. J → eV: divide.
Kinetic energy from potential difference
$$eV = \frac{1}{2}mv^2$$
- Where:
- $e$ = charge of electron (C)
- $V$ = potential difference (V)
- $m$ = mass of electron (kg)
- $v$ = velocity (m s⁻¹)
For an electron accelerated from rest through p.d. V.
Einstein's photoelectric equation
$$hf = \phi + E_{k(\max)}$$
- Where:
- $h$ = Planck's constant (J s)
- $f$ = frequency of incident radiation (Hz)
- $φ$ = work function (J)
- $E_k(max)$ = maximum kinetic energy of photoelectrons (J)
All terms must be in the same units. At the threshold: hf₀ = φ and E_k(max) = 0.
Work function from threshold frequency
$$\phi = hf_0$$
- Where:
- $φ$ = work function (J)
- $h$ = Planck's constant (J s)
- $f_0$ = threshold frequency (Hz)
Follows from the photoelectric equation when E_k(max) = 0.
Maximum kinetic energy from stopping potential
$$E_{k(\max)} = eV_s$$
- Where:
- $E_k(max)$ = maximum kinetic energy (J)
- $e$ = electron charge (C)
- $V_s$ = stopping potential (V)
Use magnitude of V_s. Stopping potential is independent of intensity.
Q1. Define one electronvoltA unit of energy equal to the energy gained by one electron accelerated through a potential difference of 1 V. 1 eV = 1.6 x 10⁻¹⁹ J..
The energy gained by an electron travelling through a potential differenceThe energy transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). of 1 V. 1 eV = 1.60 × 10⁻¹⁹ J.
Q2. How do you convert (a) eV to J and (b) J to eV?
(a) Multiply by 1.60 × 10⁻¹⁹. (b) Divide by 1.60 × 10⁻¹⁹.
Q3. What is the photoelectric effectThe emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency is incident on it.?
The emission of electrons from the surface of a metal when electromagnetic radiation of sufficiently high frequency is incident on it.
Q4. Why does the photoelectric effectThe emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency is incident on it. provide evidence for the particle nature of light?
- Each electron absorbs only one photonA quantum (discrete packet) of electromagnetic radiation. Its energy is proportional to its frequency..
- Below the threshold frequencyThe minimum frequency of incident radiation required to cause photoelectric emission from a particular metal surface., no electrons are emitted regardless of intensityThe powerThe rate of energy transfer. Measured in watts (W). transmitted per unit area perpendicular to the wave direction. Measured in W m⁻². Proportional to amplitude squared..
- A wave model predicts that any frequency should eventually cause emission if given enough time — this does not happen.
Q5. Define threshold frequency.
The minimum frequency of incident electromagnetic radiation required to remove a photoelectron from the surface of a metal.