Photoelectric Effect: Videos & Practice Problems

The photoelectric effect, as proposed by Einstein, occurs when photons with sufficient energy strike a metal surface, causing the ejection of electrons. This energy must surpass the metal's binding energy (BE), also known as threshold frequency or work function, to release an electron. Any excess photon energy is converted into the electron's kinetic energy (KE). The fundamental equation for the photoelectric effect is the energy of the photon (E_photon) equals the binding energy plus the kinetic energy:

$E_{\text{photon}}=\mathrm{BE}+\mathrm{KE}$

For calculations involving mass and velocity, KE is defined as:

$\frac{1}{2}m{v}^2$

Additionally, energy can be measured in electron volts (eV), where 1 eV equals 1.602 x 10^-19 joules, allowing for conversion between units when necessary. Understanding this effect is crucial for comprehending quantum mechanics and the behavior of light and electrons.

Photoelectric Effect

Now Einstein theorized that if a photon met an energy requirement and struck a metal surface, then electrons could be ejected. This is known as the photoelectric effect. So here if we look at it, we have a metal surface here, and on this metal surface we have free flowing electrons in green.

Now we're going to say that to this metal surface I'm going to strike it with some form of energy, here represented by energy of a photon. If it hits the surface with enough energy and enough force can dislodge one of these electrons, that electron can then convert that energy X excess energy into kinetic energy and propel itself further away from the metal surface. So this is what we call our kinetic energy.

Now for this to happen, we have to realize that when the energy of the photon or light source is greater than the energy of the surface which we're going to abbreviate as BE, then we can eject an electron. But if the energy the light source is not greater than the energy of the surface of the metal, then electron will not be ejected from that metal surface and it'll stay there.

So this is basically the idea when it comes to the photoelectric effect. Now let's click on to the next video and go a little bit more in detail about what exactly is energy KE versus energy BE.

Photoelectric Effect Formula

So we know that if enough energy is bombarded on the metal surface, it'll kick an electron off. Now we use the abbreviation BE. This stands for binding energy here. This is the minimum amount of energy needed to an eject an electron from a metal surface. And we're going to say it's also known as our threshold frequency or our work function of the metal. So it goes by a lot of different names, so binding energy, threshold frequency as well as work function.

Now kinetic energy. We say that this is the energy an object has due to its speed or motion. So basically any excess energy that the electron gains from this light source will be converted into kinetic energy. Now from this we can say that the photoelectric formula, photoelectric effect formula, is total energy, which is Ephoton, equals the binding energy plus your kinetic energy which we say is your surplus energy.

So when we're dealing with any type of photoelectric question that requires some type of calculation, it usually deals with this formula. So total energy equals binding energy plus kinetic energy.

Photoelectric Effect Example

Here we're told that the binding energy of an electrons on a metal surface are 7.15×10-19 J. If an outside energy source with 4.33×10-17 J strikes the metal surface, what would be the kinetic energy of an ejected electron?

So just remember that your total energy, which is Ephoton, equals the binding energy plus your kinetic energy. The total energy of the photon comes from this outside energy source, So that's 4.33×10-17 J equals your binding energy, which is 7.15×10-19 J plus the kinetic energy of the electron ejected.

So subtract out 7.15×10-19 J from both sides O. When we do that, we're going to get left the kinetic energy of the ejected electron. So the kinetic energy here equals 4.26×10-17 J. So this would be the energy, kinetic energy, energy of motion for that ejected electron.

Expanded Photoelectric Effect

Now the photoelectric effect formula can be expanded when we're given the additional variables of mass and velocity O. Here we're going to say with the new expanded formula that the energy of a photon can be seen as energy of a photon equals your binding energy plus your kinetic energy.

And when it comes to buying on the energy of a photon, we're going to say it's equal to Planck's constant, which is H times your frequency, which is MU binding energy. Remember is just abbreviated as BE and your kinetic energy energy of motion equals half times the mass of the electron, in this case times velocity squared.

Now sometimes you'll see instead of joules or kilojoules being used, we might see EV which stands for electron volts. So just remember here that one electron Volt equals 1.602×10-19 J. So just remember if energy is given in electron volts then use the conversion factor to change it into joules.

OK, so with our new expanded formula we could substitute this in for the energy of a photon and we could substitute this in for the kinetic energy of the ejected electron.

Work Function Calculation Example

Here it says with the surface of a metal exposed to photons at a frequency of 7.13×1016 seconds, inverse electrons are emitted with a maximum kinetic energy of 6.30×10-19 Joules. Here we need to calculate the work function of the metal. All right, So first of all, remember work function is another name for binding energy or threshold frequency. So this is EBE.

Now remember we're going to say the energy. Total energy of our photon equals binding energy, or in this case work function plus kinetic energy. In terms of energy of a photon that equals Planck's constant times your frequency O. Using that frequency given to us initially will help us to figure out the total energy of our photon.

So here those Planck's constant plug in your frequency. So when we do that, we're going to get our energy of our photon as 4.7243×10-17 joules. So take that and plug it in 4.7243×10-17 joules. Binding energy or in this case work function, is what we're looking for, and they give us the kinetic energy as 6.30×10-19 Joules.

Subtract that out from both sides and we'll have our work function at the end. So then here when we take that and plug it in, we're going to have our binding energy or our work function as equaling 4.66×10-17 Joules as our final answer for our.

A metal with a threshold frequency of 2.15 x 10¹⁵ s^-1 emits an electron with a velocity of 7.03 x 10⁶ m/s when radiation of 4.88 x 10¹⁵ s^-1 strikes the metal's surface. Calculate the mass of the electron.

• A. 6.97 x 10^-22 kg
• B. 4.98 x 10^-31 kg
• C. 2.96 x 10^-21 kg
• D. 7.32 x 10^-32 kg

Answer: (D)

An ultraviolet photon with a wavelength of 320 nm strikes a metal surface. The emitted electron has a kinetic energy of 3.0 x 10^-2 eV. What is the binding energy of the electron in kJ/mol? 1 electron volt (eV) = 1.602 x 10^-19 J.

• A. 320 kJ/mol
• B. 370 kJ/mol
• C. 450 kJ/mol
• D. 405 kJ/mol

Answer: (B)

Here’s what students ask on this topic:

What is the photoelectric effect?

The photoelectric effect is a phenomenon in physics where electrons are emitted from a material, typically a metal, when it is exposed to light of a certain frequency or above. This effect was first observed by Heinrich Hertz in 1887 and later explained by Albert Einstein in 1905, a discovery for which he was awarded the Nobel Prize in Physics in 1921.

Einstein proposed that light could be thought of as being made up of particles, or quanta, known as photons. When a photon with sufficient energy hits an electron in the metal, it transfers its energy to the electron. If this energy is greater than the work function (the minimum energy needed to remove an electron from the metal), the electron is ejected. This process demonstrates the particle-like properties of light and was crucial in the development of quantum mechanics.

The photoelectric effect has practical applications including in the development of photoelectric cells which convert light into electrical energy, forming the basis of solar panels and light-sensitive devices like automatic doors and light meters in photography.

How does the photoelectric effect support the particle theory of light?

The photoelectric effect supports the particle theory of light by demonstrating that light can behave as if it is made up of individual packets of energy, known as photons. When light of a certain frequency shines on a metal surface, it can cause electrons to be ejected from that surface. This effect can only be explained if light consists of particles, as the energy of the photons is what dislodges the electrons.

According to the wave theory of light, increasing the intensity of light (while keeping the frequency constant) should provide more energy to eject electrons. However, experiments show that no electrons are emitted if the light's frequency is below a certain threshold, regardless of the intensity. This is because the energy of the photons is too low to overcome the work function of the metal.

Albert Einstein explained this by proposing that light's energy is quantized, and each photon has an energy proportional to its frequency (E=hf). Thus, only photons with enough energy, or high enough frequency, can cause the photoelectric effect. This discovery was pivotal in establishing the concept of wave-particle duality in quantum mechanics.

Who discovered the photoelectric effect?

The photoelectric effect was first observed by a German physicist named Heinrich Hertz in 1887. While he was experimenting with electromagnetic waves, he noticed that a spark would jump between two electrodes more easily when they were illuminated by ultraviolet light. Although Hertz did not fully understand the underlying principles of this phenomenon, his observations laid the groundwork for future research.

It was Albert Einstein who, in 1905, provided a theoretical explanation for the photoelectric effect that was consistent with experimental data. Einstein proposed that light could be thought of as consisting of particles, or quanta, which we now call photons. He suggested that when these photons have enough energy, they can knock electrons out of a material. This was a significant contribution to quantum theory and one of the pivotal pieces of work that earned him the Nobel Prize in Physics in 1921. Einstein's explanation resolved the puzzle of why the photoelectric effect could not be explained by classical wave theory of light.

What is binding energy?

Binding energy refers to the energy required to separate a nucleus into its constituent protons and neutrons, or, equivalently, the energy that was released when the nucleus was formed from these nucleons. It's a measure of the stability of the nucleus; the greater the binding energy, the more stable the nucleus.

This energy is a consequence of the strong nuclear force, which is the force that holds the protons and neutrons together inside the nucleus. Because of mass-energy equivalence, as described by Einstein's famous equation:

$E=m{c}^2$

the mass of the nucleus is actually less than the sum of the individual masses of the protons and neutrons. This difference in mass, known as the mass defect, is converted into binding energy when the nucleus is formed.

In nuclear reactions, such as fission or fusion, a portion of the binding energy can be released as usable energy, which is the principle behind nuclear power and atomic weapons. Understanding binding energy is crucial for studying nuclear physics and various applications in energy production and medical technologies.