Stopping Voltage in Photoelectric Effect Calculator

The photoelectric effect is a crucial phenomenon in quantum physics, illustrating the particle nature of light. When light hits a metal surface, it can eject electrons from the metal, a process that depends on the light's frequency and the metal's work function.

Historical Background

The photoelectric effect was first observed by Heinrich Hertz in 1887, but it was Albert Einstein who, in 1905, provided its theoretical explanation, for which he won the Nobel Prize in Physics in 1921. Einstein proposed that light consists of quanta, or photons, whose energy depends on their frequency.

Calculation Formula

The stopping voltage (\(ΔV_0\)) in the photoelectric effect is calculated using the formula:

\[ ΔV_0 = \frac{hf - Φ}{e} \]

where:

• \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J·s}\)),
• \(f\) is the frequency of the incident photon,
• \(Φ\) is the work function of the metal,
• \(e\) is the charge of an electron (\(1.6 \times 10^{-19} \, \text{C}\)).

Example Calculation

Given:

• Frequency of incident photon (\(f\)) = 0.12456 Hz,
• Work function of metal (\(Φ\)) = \(7.2098 \times 10^{-19}\) J,

The stopping voltage (\(ΔV_0\)) is calculated as:

\[ ΔV_0 = \frac{(6.626 \times 10^{-34} \times 0.12456) - 7.2098 \times 10^{-19}}{1.6 \times 10^{-19}} \]

\[ ΔV_0 = -4.506124999999999 \, \text{V} \]

Importance and Usage Scenarios

The photoelectric effect is pivotal for understanding quantum mechanics and has practical applications in photovoltaic cells, photoelectron spectroscopy, and the development of electronic devices like photodiodes.

Common FAQs

1. What is the work function of a metal?

   • The work function is the minimum energy required to remove an electron from the surface of a metal.

2. How does the frequency of light affect the photoelectric effect?

   • The energy of the incident photons must exceed the work function of the metal for electrons to be ejected. Higher frequency (and thus energy) photons can increase the kinetic energy of ejected electrons.

3. Can any frequency of light cause the photoelectric effect in a metal?

   • No, there is a minimum threshold frequency below which no electrons are ejected, regardless of the light's intensity.

This calculator provides a simple way to understand and calculate the stopping voltage in the photoelectric effect, bridging concepts in quantum mechanics with practical applications in modern technology.