11TH GRADE · QUANTUM PHYSICS

Photons and the photoelectric effect

Photon energy and momentum, photoelectric effect equation and red boundary.

30 minutes27 theory cards

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LESSON MATERIAL

Basic Concepts

Photon

A quantum of electromagnetic radiation that transfers energy and momentum.

The photon has no rest frame and non-zero rest mass: its energy E = hν, and its momentum p = h/λ.

Photo effect

The emission of electrons by a substance under the influence of electromagnetic radiation.

One photon transfers energy to one electron: frequency determines the possibility of exit and the energy of the electron, intensity determines the number of electrons.

red photo effect border

The lowest frequency or longest wavelength at which the photoelectric effect is still possible.

Below the threshold frequency, the photoelectric effect will not begin even at very high light intensity.

LESSON MATERIAL

Physical quantities

Photon energy

E

The energy of one quantum of electromagnetic radiation.

Unit: joule · $\mathrm{Dzh}$

Planck's constant

h

Coefficient of coupling between photon energy and frequency.

Unit: joule second · $\mathrm{Dzh}\cdot\mathrm{s}$

Emission frequency

\nu

The number of oscillations of the electromagnetic field per unit time.

Unit: hertz · $\mathrm{Gts}$

Mass equivalent of photon energy

m_{\gamma}

Ratio of photon energy to c²; this is not the rest mass, which is zero for a photon.

Unit: kilogram · $\mathrm{kg}$

Photon rest mass

m_0

The invariant rest mass of a photon is zero; the value E/c² is not the rest mass.

Unit: kilogram · $\mathrm{kg}$

Photon momentum

p

A measure of the translational motion of a photon.

Unit: kilogram-meter per second · $\frac{\mathrm{kg}\cdot\mathrm{m}}{\mathrm{s}}$

Work function

A

Minimum energy to remove an electron from the surface of a substance.

Unit: joule · $\mathrm{Dzh}$

Photoelectron kinetic energy

E_{\text{k}}

The energy of motion of an electron after leaving a substance.

Unit: joule · $\mathrm{Dzh}$

Photoelectron mass

m

The mass of an electron emitted during the photoelectric effect.

Unit: kilogram · $\mathrm{kg}$

Electron charge modulus

\lvert e\rvert

Positive value of the modulus of the electric charge of an electron.

Unit: pendant · $\mathrm{Kl}$

Holding voltage

U_{\text{z}}

The voltage at which the fastest photoelectrons stop reaching the anode.

Unit: volt · $\mathrm{V}$

Threshold frequency

\nu_0

Minimum frequency of light for the photoelectric effect.

Unit: hertz · $\mathrm{Gts}$

Red border by wavelength

\lambda_0

The maximum wavelength of light that causes the photoelectric effect.

Unit: meter · $\mathrm{m}$

LESSON MATERIAL

Lesson formulas

Photon energy

E=h\nu=\frac{hc}{\lambda}

The energy of a photon increases with frequency and decreases with wavelength.

Condition: For a photon in a vacuum; The rest mass of the photon is zero.

Mass equivalent of photon energy

m_{\gamma}=\frac{E}{c^2}

The energy of a photon can be formally compared to a mass equivalent, but this is not the rest mass of the photon.

Photon momentum

p=\frac{E}{c}=\frac{h}{\lambda}

The momentum of a photon is determined by its energy or wavelength.

Condition: For a photon in vacuum.

Planck's constant

h=6{,}62\cdot10^{-34}\,\mathrm{Dzh}\cdot\mathrm{s}

Planck's constant sets the quantum scale of action.

Speed of light

c=3\cdot10^8\,\frac{\mathrm{m}}{\mathrm{s}}

The speed of light in a vacuum is approximately three hundred million meters per second.

Electronvolt to joules

1\,\mathrm{eV}=1{,}6\cdot10^{-19}\,\mathrm{Dzh}

One electron volt is equal to the charge energy of an electron when passing through a potential difference of one volt.

Einstein's equation for the photoelectric effect

E=A+E_{\text{k}}

The photon energy is spent on the work function and kinetic energy of the electron.

Photoelectron kinetic energy

E_{\text{k}}=\frac{mv^2}{2}=\lvert e\rvert U_{\text{z}}

The maximum kinetic energy is related to the speed of the electron and the retardation voltage.

Red limit for energy

h\nu_0=A

At the red boundary, the photon energy is exactly equal to the work function.

Threshold frequency of photoelectric effect

\nu_0=\frac{A}{h}

The minimum frequency is determined by the work function and Planck's constant.

Red border by wavelength

\lambda_0=\frac{c}{\nu_0}

The maximum wavelength is related to the speed of light and the threshold frequency.

Related formulas

WorkA · J Frequencyν · Hz EnergyE, W · J

PRACTICE

Tasks on the topic

Quantum physics11 class · 17 problems