Intensity↑ = photocurrent↑ (number of electrons). The maximum kinetic energy does not change.
When reverse voltage ≥ stopping potential Vs, electrons cannot reach the anode and the photocurrent is zero.
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Results
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Photon energy hf [eV]
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Work function φ [eV]
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Maximum kinetic energy [eV]
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Stopping potential Vs [V]
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Threshold frequency f₀ [×10¹⁴Hz]
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Threshold wavelength λ₀ [nm]
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Photocurrent I (relative)
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Reverse voltage [V]
Visualization
Theory & Key Formulas
KE_max = hf − φ
0.00 eV
Photocurrent I (varies with intensity)
0.0
Moving the intensity slider changes the right bar (photocurrent), but the left bar (KE_max) remains unchanged. Increasing the frequency extends the left bar. This is the essence of quantum theory.
Graph
Theory & Key Formulas
$$K_{max} = hf - \phi$$ $h = 6.626 \times 10^{-34}$ J·s (Planck's constant)
$f$: light frequency (Hz), $\phi$: work function (J), $K_{max}$: maximum kinetic energy (J)
Threshold frequency: $f_0 = \phi/h$ (no electrons are emitted below this frequency)
Stopping voltage and photocurrent
Stopping potential: $eV_s = K_{max} = hf - \phi$
Photocurrent is proportional to the number of photons (light intensity), while the maximum electron speed ($K_{max}$) depends only on frequency
$\lambda = c/f$ (wavelength), visible light: 380–700 nm
FAQ
Why does the photoelectric effect demonstrate the particle nature of light?
Classical wave theory predicts that increasing light intensity should eject electrons. But electrons are only emitted above a threshold frequency, proving light comes in discrete energy packets hf.
Why does increasing intensity not increase maximum kinetic energy?
Intensity corresponds to photon count. More photons eject more electrons but each photon energy hf stays the same, so maximum kinetic energy is unchanged.
Did Einstein win the Nobel Prize for the photoelectric effect?
Yes. Einstein received the 1921 Nobel Prize in Physics specifically for discovering the law of the photoelectric effect, not relativity.
How does the photoelectric effect relate to solar cells?
Solar cells also use photon absorption to excite electrons, but occur in p-n semiconductor junctions rather than at a metal surface.
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I can see the simulation updating, but what exactly is being calculated here?
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Great question! The simulator solves the governing equations in real time as you move the sliders. Each parameter you control directly affects the physical outcome you see in the graph. The key is to build an intuitive feel for how each variable influences the result — that's how engineers develop physical judgment.
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So when I increase this parameter, the curve shifts significantly. Is that a linear relationship?
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It depends on the model. Some relationships are linear, but many engineering phenomena are nonlinear. Try moving the sliders to extreme values and see if the output changes proportionally — if the graph shape changes, that's a sign of nonlinearity. This hands-on exploration is exactly what simulations are best for.
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Where is this kind of analysis actually used in practice?
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Constantly! Engineers run these calculations during the design phase to quickly screen parameters before investing in expensive physical tests or detailed finite element simulations. Getting comfortable with these simplified models is a real engineering skill.
Set light frequency using the frequency slider (sF) or numeric input (sFNum), ranging from 4.0×10¹⁴ Hz to 8.0×10¹⁴ Hz
Adjust light intensity with the intensity slider (sI) or numeric input (sINum), from 0.5 to 5.0 W/m²
Observe the stopping voltage output (vWNum) and work function display (sWNum); electrons only emit when frequency exceeds the threshold frequency f₀=W/h
Vary parameters to identify that stopping voltage depends on frequency but not intensity: Vs = (hf - W)/e
Worked Example
For sodium metal (work function W=2.28 eV), set frequency to 6.5×10¹⁴ Hz with intensity 2.0 W/m². Using h=6.626×10⁻³⁴ J·s and e=1.602×10⁻¹⁹ C, the photon energy equals 4.31×10⁻¹⁹ J (2.69 eV), exceeding sodium's threshold. The stopping voltage calculates as Vs=(2.69−2.28)/1=0.41 V. Increasing intensity to 4.0 W/m² produces identical stopping voltage but doubles photocurrent, demonstrating intensity affects electron count, not kinetic energy.
Practical Notes
Threshold frequency for common metals: tungsten (1.39×10¹⁵ Hz, W=5.5 eV), copper (1.23×10¹⁵ Hz, W=4.7 eV), zinc (9.84×10¹⁴ Hz, W=3.74 eV)
Below threshold frequency, photocurrent remains zero regardless of intensity—this contradicts classical wave theory and proves photon quantization
Stopping voltage directly measures maximum kinetic energy: KEmax = eVs, essential for determining Planck constant experimentally