This is a statement of conservation of energy
Quantum Physics - OCR A-Level Physics
$$hf = \phi + KE_{max}$$
- This is a statement of conservation of energyThe capacity to do work. Measured in joules (J).Energy cannot be created or destroyed, only transferred from one form to another. The total energyThe capacity to do work. Measured in joules (J). of a closed system remains constant.: photonA quantum (discrete packet) of electromagnetic radiation. Its energy is proportional to its frequency. $energyThe capacity to do work. Measured in joules (J). = work functionThe minimum energy required to liberate an electron from the surface of a metal. + maximum kinetic energyThe energy an object possesses due to its motion.$ of the emitted electron.
- KE_max is the maximum kinetic energyThe energy an object possesses due to its motion. because surface electrons require the least energy to escape. Electrons deeper in the metal lose more energy before reaching the surface.
- At the 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.: $hf_{0} = \phi$, so $KE_{\max} = 0$.
- A graph of KE_max vs frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). f is a straight line with gradient h (Planck constant), x-intercept at f₀ (threshold frequencyThe minimum frequency of incident radiation required to cause photoelectric emission from a particular metal surface.), and y-intercept at −φ.
$$\begin{aligned}
eV_s &= KE_{max} \\
&= hf - \phi
\end{aligned}$$
- The stopping potentialThe minimum 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). required to stop the most energetic photoelectrons emitted in the photoelectric effectThe emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency is incident on it.. V_s is the minimum p.d. needed to reduce the photocurrent to zero, stopping the most energetic photoelectrons.
Worked Example [3 marks]
The work functionThe minimum energy required to liberate an electron from the surface of a metal. of sodium is 2.3 eV. UV light of frequency 8.0 × 10¹⁴ Hz is incident on a sodium surface. Calculate the maximum kinetic energyThe energy an object possesses due to its motion. of the emitted photoelectrons in eV.
Show Solution
1
PhotonA quantum (discrete packet) of electromagnetic radiation. Its energy is proportional to its frequency. energy
$E = hf = 6.63 \times 10⁻^{3}⁴ \times 8.0 \times 10¹⁴ = 5.30 \times 10⁻¹⁹ J$
[1]2
Convert to eV
$E = 5.30 \times 10⁻¹⁹ / 1.6 \times 10⁻¹⁹ = 3.31 eV$
[1]3
$KE_max = hf - \phi = 3.31 - 2.3 = 1.0 eV$
[1]Answer
KE_max = 1.0 eV
Worked Example [2 marks]
Calculate the threshold frequencyThe minimum frequency of incident radiation required to cause photoelectric emission from a particular metal surface. for a metal with work functionThe minimum energy required to liberate an electron from the surface of a metal. 4.0 × 10⁻¹⁹ J.
Show Solution
1
At threshold
$hf_{0} = \phi, so f_{0} = \phi/h = (4.0 \times 10⁻¹⁹) / (6.63 \times 10⁻^{3}⁴)$
[1]2
$f_{0} = 6.03 \times 10¹⁴ Hz$
[1]Answer
$f_{0} = 6.0 \times 10¹⁴ Hz$