What is the Photoelectric Effect Calculator?
Quick Answer: An interactive tool that uses Einstein's photoelectric equation (E = W + K_max) to compute maximum kinetic energy, stopping potential, and work function from incident light wavelength/frequency. It visualizes the kinetic energy vs. frequency graph with the threshold frequency marked.
Theory of the Photoelectric Effect
The photoelectric effect occurs when light of sufficient energy strikes a metal surface and ejects electrons. Einstein's equation:
E_photon = hf = W + K_max
where h = 6.626e-34 J·s (Planck's constant), f is frequency, W is the work function (minimum energy to eject an electron), and K_max is the maximum kinetic energy of emitted electrons.
K_max is also related to the stopping potential V_0: K_max = eV_0 (e = 1.602e-19 C).
The threshold frequency f_0 = W/h. No electrons are emitted if f < f_0.
The graph displays K_max (in eV) vs. frequency, showing a linear relationship with slope h. The x-intercept gives f_0.
Step-by-Step Examples
Example 1: Sodium Metal
- Set work function to 2.3 eV (sodium). Enter wavelength = 400 nm.
- Photon energy = 1240/400 = 3.10 eV. K_max = 3.10 - 2.3 = 0.80 eV. Stopping potential = 0.80 V.
- The graph shows a data point above threshold. Adjust wavelength to 600 nm (2.07 eV) — no emission, K_max=0.
Example 2: Finding Threshold Frequency
- Keep work function 2.3 eV. Threshold frequency f_0 = 2.3 * 1.602e-19 / 6.626e-34 = 5.56e14 Hz.
- Set frequency slider to 5.6e14 Hz; photon energy equals work function, K_max = 0.
Example 3: Exploring Different Metals
- Try work function 4.5 eV (platinum). Use UV light (200 nm). Observe higher threshold, larger stopping potential.
Frequently Asked Questions
What units are used?
Wavelength in nanometers (nm), frequency in Hertz (Hz), work function and K_max in electronvolts (eV). Planck's constant h = 6.626e-34 J.s, 1 eV = 1.602e-19 J.
Why does K_max become zero for long wavelengths?
If photon energy (hf) is less than the work function, no electrons are emitted, so K_max = 0. The tool correctly caps K_max at zero.
How is the graph generated?
It plots K_max (eV) vs. frequency (Hz) for the selected work function. The line has a slope of h/e (in eV/Hz), and the x-intercept is the threshold frequency f_0 = W/h.
Can I use frequency instead of wavelength?
Yes, directly enter frequency. The wavelength input will update automatically (c = fλ). Changing one recalculates the other.
Is the classical wave theory prediction shown?
No, this tool strictly follows Einstein's photon theory, which accurately describes the effect. Classical predictions are not simulated.