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Photoelectric Effect Calculator

Calculate photoelectron energy, stopping potential, and threshold wavelength for the photoelectric effect

Parameters

nmⓘ
eVⓘ
W/m²ⓘ
Show Trail

Controls

xⓘ

Calculated Values

Photon Energy:
3.10;eV3.10;eV
Max Kinetic Energy:
1.10;eV1.10;eV
Stopping Potential:
1.10;V1.10;V
Threshold Wavelength:
619.92;nm619.92;nm
Threshold Frequency:
483597848416983.63;Hz483597848416983.63;Hz

Examples

Example 1: Visible Light on Metal

Blue light (400 nm) incident on a metal with work function 2.0 eV.

  • Photon Energy: 3.103.10
  • Max Kinetic Energy: 1.101.10
  • Stopping Potential: 1.101.10

Example 2: UV Light

Ultraviolet light (200 nm) on the same metal.

  • Photon Energy: 6.206.20
  • Max Kinetic Energy: 4.204.20
  • Stopping Potential: 4.204.20

Example 3: Below Threshold

Red light (700 nm) on the same metal (below threshold).

  • Photon Energy: 1.771.77
  • Max Kinetic Energy: 0.000.00
  • Stopping Potential: 0.000.00

Visualization

Photoelectric Effect

The photoelectric effect is a fundamental quantum phenomenon where electrons are ejected from a material's surface when exposed to electromagnetic radiation of sufficient energy. This effect provided crucial evidence for the quantum nature of light and helped establish quantum mechanics.

Einstein's photoelectric equation states that the maximum kinetic energy of ejected electrons is K_max = hf - φ, where h is Planck's constant, f is the frequency of incident light, and φ is the work function of the material. The work function represents the minimum energy required to remove an electron from the material.

Key features of the photoelectric effect include: (1) A threshold frequency below which no electrons are emitted, regardless of intensity; (2) The maximum kinetic energy of electrons depends only on frequency, not intensity; (3) The number of electrons emitted is proportional to the light intensity; (4) Electron emission is instantaneous when light hits the surface.

The photoelectric effect has numerous applications, including photodiodes, solar cells, photomultiplier tubes, and various imaging technologies. It's fundamental to understanding quantum optics, spectroscopy, and the interaction of light with matter.

The stopping potential is the minimum voltage required to prevent electrons from reaching the anode, given by V_stop = K_max/e, where e is the elementary charge. This provides a direct way to measure the maximum kinetic energy of photoelectrons.

Key Concepts

  • Einstein's Equation: K_max = hf - φ = hc/λ - φ
  • Work Function: Minimum energy to remove an electron
  • Threshold Frequency: f_threshold = φ/h
  • Threshold Wavelength: λ_threshold = hc/φ
  • Stopping Potential: V_stop = K_max/e
  • Photon Energy: E = hf = hc/λ

Real-World Applications

  • Solar Cells: Converting light energy to electrical energy
  • Photodiodes: Light detection and measurement
  • Photomultiplier Tubes: Amplifying weak light signals
  • Digital Cameras: Image sensors and CCD arrays
  • Spectroscopy: Analyzing material composition

Explore Further

More modern physics tools

Physics Equations

Einstein's Equation:
Kmax=hf−ϕ=hcλ−ϕK_{max} = hf - \phi = \frac{hc}{\lambda} - \phi
Photon Energy:
E=hf=hcλE = hf = \frac{hc}{\lambda}
Stopping Potential:
Vstop=KmaxeV_{stop} = \frac{K_{max}}{e}
Threshold Wavelength:
λthreshold=hcϕ\lambda_{threshold} = \frac{hc}{\phi}
Threshold Frequency:
fthreshold=ϕhf_{threshold} = \frac{\phi}{h}

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Calculate Photon Energy

First, we calculate the energy of each incident photon:

Equation:

E=hcλE = \frac{hc}{\lambda}

Calculation:

E=6.63e−34×3.00e+84.00e−7=3.10 eVE = \frac{6.63e-34 \times 3.00e+8}{4.00e-7} = 3.10 \text{ eV}

Explanation:

This is the energy carried by each photon of the incident light.

2

Step 2: Calculate Maximum Kinetic Energy

Using Einstein's photoelectric equation:

Equation:

Kmax=hf−ϕ=E−ϕK_{max} = hf - \phi = E - \phi

Calculation:

Kmax=3.10−2.00=1.10 eVK_{max} = 3.10 - 2.00 = 1.10 \text{ eV}

Explanation:

This gives the maximum kinetic energy of ejected electrons.

3

Step 3: Calculate Stopping Potential

The stopping potential is related to the maximum kinetic energy:

Equation:

Vstop=KmaxeV_{stop} = \frac{K_{max}}{e}

Calculation:

Vstop=1.10 eV1 eV/V=1.10 VV_{stop} = \frac{1.10 \text{ eV}}{1 \text{ eV/V}} = 1.10 \text{ V}

Explanation:

This is the voltage needed to stop the fastest electrons.

4

Step 4: Calculate Threshold Wavelength

The threshold wavelength for this material is:

Equation:

λthreshold=hcϕ\lambda_{threshold} = \frac{hc}{\phi}

Calculation:

λthreshold=6.63e−34×3.00e+83.20e−19=620 nm\lambda_{threshold} = \frac{6.63e-34 \times 3.00e+8}{3.20e-19} = 620 \text{ nm}

Explanation:

Light with longer wavelength cannot eject electrons from this material.

Frequently Asked Questions (FAQ)

What is the photoelectric effect?

The photoelectric effect is the emission of electrons from a material's surface when exposed to electromagnetic radiation of sufficient energy, providing evidence for the quantum nature of light.

What is the work function?

The work function is the minimum energy required to remove an electron from a material's surface. It's a characteristic property of the material and represents the binding energy of the most loosely bound electrons.

Why doesn't intensity affect electron energy?

Intensity affects the number of photons (and thus the number of electrons), but each photon transfers its energy to a single electron. The energy of each electron depends only on the photon energy minus the work function.

What is the threshold frequency?

The threshold frequency is the minimum frequency of light required to eject electrons from a material. Below this frequency, no electrons are emitted regardless of intensity.

What is the stopping potential?

The stopping potential is the minimum voltage required to prevent photoelectrons from reaching the anode. It's directly related to the maximum kinetic energy of the ejected electrons.

Practice MCQs

  1. According to Einstein's photoelectric equation, the maximum kinetic energy of photoelectrons is:
  2. If the wavelength of incident light is doubled, the photon energy becomes:
  3. The threshold wavelength for a material is:
  4. What happens if the incident light has energy less than the work function?
  5. The stopping potential is related to the maximum kinetic energy by:

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