Einstein's Photoelectric Equation:
The equation states that the kinetic energy (KE) of an emitted electron is equal to the energy of the incident photon (hν) minus the work function (Φ) of the metal:
KE = hν - Φ
Where:
* KE: Kinetic energy of the emitted electron
* h: Planck's constant (6.63 × 10⁻³⁴ J·s)
* ν: Frequency of the incident radiation
* Φ: Work function of the metal (the minimum energy required to remove an electron from the metal surface)
Explanation:
1. Work Function: The work function (Φ) represents the energy binding an electron to the metal. It's a specific value for each metal.
2. Photon Energy: The energy of a photon is directly proportional to its frequency (E = hν).
3. Threshold Frequency: For an electron to be emitted, the photon's energy (hν) must be greater than or equal to the work function (Φ). This means there's a minimum frequency (ν₀) below which no electrons will be emitted, regardless of the intensity of the light. This is known as the threshold frequency.
Why Frequency Matters:
* Below Threshold Frequency: If the frequency of the incident radiation is less than the threshold frequency (ν < ν₀), the photon's energy is insufficient to overcome the work function. Consequently, no electrons are emitted, even if the light intensity is high.
* At Threshold Frequency: When the frequency reaches the threshold frequency (ν = ν₀), the photon's energy is exactly equal to the work function. Electrons are emitted, but they have zero kinetic energy (KE = 0).
* Above Threshold Frequency: If the frequency is higher than the threshold frequency (ν > ν₀), the photon has enough energy to overcome the work function and provide additional kinetic energy to the emitted electron. The higher the frequency, the greater the kinetic energy of the emitted electrons.
In Conclusion:
The Einstein photoelectric equation explains the frequency dependence of the photoelectric effect because it establishes a direct relationship between the energy of the incident photon and the work function of the metal. The equation elegantly demonstrates that electrons are only ejected when the photon's energy is sufficient to overcome the binding energy of the metal, which is directly tied to the frequency of the light.
