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Photoelectric Effect Lab

Shine light on different metal surfaces and observe whether electrons are emitted. Adjust the frequency to cross the threshold, change the metal to see different work functions, and discover why intensity affects electron count but not kinetic energy. Every calculation follows Einstein's photoelectric equation step by step.

Visualization

Metalφ = 2.1 eVLight (461 nm)eeeeeeeeee10 electrons emittedIRVisibleUV

Parameters

Hz

= 461.2 nm

InfraredVisibleUV

Intensity affects electron count, not kinetic energy.

Results

Photon energy (E = hf)
2.6882 eV
Work function (φ) for Cesium
2.1 eV
Threshold frequency (f₀)
5.078 × 10^14 Hz
Threshold wavelength (λ₀)
590.4 nm
Max kinetic energy (KEₘₐₓ)
0.5882 eV
Stopping voltage (V₀)
0.5882 V
Electrons emitted
10
Electrons are emitted with maximum KE = 0.5882 eV.

KE vs Frequency Graph

f₀05e1410e1415e1420e14-1012345Frequency (Hz)KE_max (eV)KE = hf − φNo emission (KE = 0)

Step-by-Step Calculation

1. Photon energy

E=hfE = hf
E=(4.136×10−15)(6.5×1014)E = (4.136 \times 10^{-15})(6.5 \times 10^{14})
E=2.6882 eVE = 2.6882 \text{ eV}

2. Threshold frequency for Cesium

f0=ϕhf_0 = \frac{\phi}{h}
f0=2.14.136×10−15f_0 = \frac{2.1}{4.136 \times 10^{-15}}
f0=5.078×1014 Hzf_0 = 5.078 \times 10^{14} \text{ Hz}

3. Check emission condition

Emission occurs when E>ϕ\text{Emission occurs when } E > \phi
2.6882 eV>2.1 eV2.6882 \text{ eV} > 2.1 \text{ eV}
Emission occurs!\text{Emission occurs!}

4. Maximum kinetic energy (Einstein's equation)

KEmax=hf−ϕKE_{\text{max}} = hf - \phi
KEmax=2.6882−2.1KE_{\text{max}} = 2.6882 - 2.1
KEmax=0.5882 eVKE_{\text{max}} = 0.5882 \text{ eV}

5. Stopping voltage

V0=KEmaxeV_0 = \frac{KE_{\text{max}}}{e}
V0=0.5882 eVeV_0 = \frac{0.5882 \text{ eV}}{e}
V0=0.5882 VV_0 = 0.5882 \text{ V}

Reference Guide

Einstein's Photoelectric Equation

Einstein explained the photoelectric effect by treating light as packets of energy (photons). Each photon carries energy proportional to its frequency.

KEmax=hf−ϕKE_{\text{max}} = hf - \phi

where h=4.136×10−15  eV⋅sh = 4.136 \times 10^{-15}\;\text{eV}\cdot\text{s} is Planck's constant and ϕ\phi is the work function of the metal.

Threshold Frequency

Below a certain frequency, no electrons are emitted regardless of how bright the light is. This minimum frequency depends only on the metal.

f0=ϕhf_0 = \frac{\phi}{h}

Cesium has a low work function (2.1 eV), so visible light can eject electrons. Platinum requires ultraviolet light because its work function is 5.65 eV.

Intensity vs Frequency

This is the key insight that classical physics could not explain. Increasing the light intensity (brightness) increases the number of photons hitting the surface, so more electrons are emitted. But each electron's kinetic energy depends only on the photon frequency, not the intensity.

A dim ultraviolet light can eject electrons that a bright red light cannot.

Stopping Voltage

The stopping voltage is the minimum reverse voltage needed to stop the most energetic photoelectrons.

V0=KEmaxe=hf−ϕeV_0 = \frac{KE_{\text{max}}}{e} = \frac{hf - \phi}{e}

By measuring the stopping voltage at different frequencies, you can determine Planck's constant experimentally. The slope of the V0V_0 vs ff graph equals h/eh/e.