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

Einstein's theory of the photoelectric effect describes how photons can cause the ejection of electrons from a metal surface when certain energy conditions are met. In this phenomenon, a photon, which is a particle of light, strikes a metal surface that contains free-flowing electrons. If the energy of the incoming photon exceeds the binding energy (denoted as \( E_b \)) of the electrons in the metal, it can dislodge an electron from the surface.

When a photon with sufficient energy collides with the metal, it transfers its energy to an electron. If the energy of the photon is greater than \( E_b \), the excess energy is converted into kinetic energy (\( KE \)) of the ejected electron, allowing it to move away from the metal surface. The relationship can be expressed as:

\[ KE = E_{photon} - E_b \]

Here, \( KE \) represents the kinetic energy of the ejected electron, \( E_{photon} \) is the energy of the incoming photon, and \( E_b \) is the binding energy of the electron in the metal. If the energy of the photon is less than or equal to \( E_b \), the electron remains bound to the metal surface and is not ejected.

This principle is fundamental in understanding the interaction between light and matter, illustrating how light can influence the behavior of electrons in conductive materials.

Photoelectric Effect Formula

The photoelectric effect describes the phenomenon where electrons are ejected from a metal surface when it is exposed to sufficient energy, typically in the form of light. The minimum energy required to release an electron from the surface is referred to as binding energy (BE), which is also known as the threshold frequency or work function of the metal. This energy is crucial for understanding how light interacts with matter.

Kinetic energy (KE) is the energy that an object possesses due to its motion. In the context of the photoelectric effect, any excess energy that an electron absorbs from the incident light beyond the binding energy is converted into kinetic energy. This relationship can be expressed through the photoelectric effect formula:

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

In this equation, \(E_{\text{photon}}\) represents the total energy of the incoming photon, \(BE\) is the binding energy, and \(KE\) is the kinetic energy of the ejected electron. When solving problems related to the photoelectric effect, this formula is essential for calculating the energies involved and understanding the behavior of electrons when exposed to light.

Photoelectric Effect Example

The binding energy of electrons on a metal surface is a crucial concept in understanding the photoelectric effect. In this scenario, the binding energy is given as \(7.15 \times 10^{-19}\) joules. When an external energy source delivers \(4.33 \times 10^{-17}\) joules to the metal surface, we can determine the kinetic energy of an ejected electron using the relationship between the total energy of the photon, the binding energy, and the kinetic energy of the electron.

The equation governing this relationship is:

\[ E_{\text{photon}} = E_{\text{binding}} + KE \]

Here, \(E_{\text{photon}}\) represents the total energy from the external source, \(E_{\text{binding}}\) is the binding energy, and \(KE\) is the kinetic energy of the ejected electron. By substituting the known values into the equation, we have:

\[ 4.33 \times 10^{-17} \, \text{J} = 7.15 \times 10^{-19} \, \text{J} + KE \]

To isolate the kinetic energy, we subtract the binding energy from both sides:

\[ KE = 4.33 \times 10^{-17} \, \text{J} - 7.15 \times 10^{-19} \, \text{J} \]

Calculating this gives:

\[ KE = 4.26 \times 10^{-17} \, \text{J} \]

This result indicates that the kinetic energy of the ejected electron is \(4.26 \times 10^{-17}\) joules, representing the energy of motion for the electron after overcoming the binding energy. Understanding this relationship is essential in fields such as quantum mechanics and materials science, where the behavior of electrons in metals is a fundamental aspect of study.

Expanded Photoelectric Effect

The photoelectric effect describes how light can eject electrons from a material, and its formula can be expanded to include additional variables such as mass and velocity. The energy of a photon can be expressed as:

E_photon = B.E. + K.E.

In this equation, E_photon represents the energy of the photon, B.E. is the binding energy, and K.E. is the kinetic energy of the ejected electron. The binding energy can be calculated using Planck's constant (h) multiplied by the frequency (ν) of the photon:

B.E. = hν

The kinetic energy, which represents the energy of motion, is given by the formula:

K.E. = ½mv²

Here, m is the mass of the electron, and v is its velocity. It's important to note that energy can be expressed in different units. While joules (J) are commonly used, energy may also be represented in electron volts (eV). The conversion between these units is defined as:

1 eV = 1.602 × 10^-19 J

When working with energy values in electron volts, it is essential to convert them to joules using this conversion factor. By substituting the expressions for binding energy and kinetic energy into the expanded formula, one can analyze the energy dynamics involved in the photoelectric effect more comprehensively.

Work Function Calculation Example

To determine the work function of a metal when exposed to photons, we can utilize the relationship between the energy of the incoming photons, the work function, and the kinetic energy of the emitted electrons. The work function, often denoted as \( \phi \), represents the minimum energy required to remove an electron from the surface of the metal.

In this scenario, the frequency of the photons is given as \( 7.13 \times 10^{16} \, \text{s}^{-1} \), and the maximum kinetic energy of the emitted electrons is \( 6.30 \times 10^{-19} \, \text{J} \).

First, we calculate the energy of the incoming photons using the formula:

\[ E_{\text{photon}} = h \cdot f \]

where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \)) and \( f \) is the frequency. Plugging in the values:

\[ E_{\text{photon}} = (6.626 \times 10^{-34} \, \text{J s}) \cdot (7.13 \times 10^{16} \, \text{s}^{-1}) \approx 4.7243 \times 10^{-17} \, \text{J} \]

Next, we apply the energy conservation principle, which states that the total energy of the photon is equal to the work function plus the kinetic energy of the emitted electron:

\[ E_{\text{photon}} = \phi + KE \]

Rearranging this equation to solve for the work function gives us:

\[ \phi = E_{\text{photon}} - KE \]

Substituting the known values:

\[ \phi = 4.7243 \times 10^{-17} \, \text{J} - 6.30 \times 10^{-19} \, \text{J} \approx 4.6610 \times 10^{-17} \, \text{J} \]

Thus, the work function of the metal is approximately \( 4.66 \times 10^{-17} \, \text{J} \). This value indicates the energy barrier that must be overcome for an electron to be emitted from the metal surface when exposed to light of the specified frequency.

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.