A photon is the smallest packet of light energy. Think of it as a tiny, invisible ball that can behave like a wave or a particle, depending on the experiment. 🌟
Photons carry energy that depends on how fast they oscillate – their frequency. The relationship is:
\$E = h\nu\$
Even though photons have no mass, they still carry momentum:
\$p = \frac{h}{\lambda}\$
In the photoelectric effect, electrons are ejected from a metal only if the incoming photons have a minimum frequency, called the threshold frequency (\$\nu_0\$). The condition is:
\$h\nu_0 = \phi\$
Because frequency and wavelength are inversely related (\$c = \nu\lambda\$), we can also talk about a threshold wavelength (\$\lambda_0\$). The relationship is:
\$\lambda0 = \frac{c}{\nu0}\$
| Property | Formula | What It Means |
|---|---|---|
| Energy | \$E = h\nu\$ | Higher frequency → more energy. |
| Momentum | \$p = \dfrac{h}{\lambda}\$ | Shorter wavelength → larger momentum. |
| Threshold Frequency | \$h\nu_0 = \phi\$ | Minimum frequency to eject electrons. |
| Threshold Wavelength | \$\lambda0 = \dfrac{c}{\nu0}\$ | Longest wavelength that can still eject electrons. |
Remember the work function: \$\phi\$ is always given in joules (J) or electron‑volts (eV). Convert units if needed.
Use the speed of light: \$c = 3.00\times10^8\ \text{m/s}\$ to switch between frequency and wavelength.
Check units: Energy in J, frequency in Hz, wavelength in m, momentum in kg·m/s.
📚 Practice converting between \$E\$, \$\nu\$, and \$\lambda\$ using the formulas above.
Imagine a photon as a tiny, glowing marble that can bounce off a surface. If the marble is heavy (high energy), it can knock other marbles (electrons) off the surface. If it’s light (low energy), it just glides by. The threshold frequency is like the minimum weight the marble needs to lift another marble.