Stopping potential
Stopping Potential
Stopping potential in the context of physics, particularly in the study of the photoelectric effect, is a fundamental concept that helps us understand how photons interact with electrons in a material.
Understanding Stopping Potential
When light of a certain frequency shines on a metal surface, it can cause electrons to be ejected from the surface. This phenomenon is known as the photoelectric effect. The ejected electrons have kinetic energy that depends on the frequency of the incident light and the material of the metal. The stopping potential is the minimum reverse voltage needed to stop the most energetic photoelectrons from reaching the anode in a photoelectric experiment.
The Photoelectric Equation
The kinetic energy of the ejected electrons can be described by the photoelectric equation:
[ KE_{\text{max}} = h\nu - \phi ]
where:
- ( KE_{\text{max}} ) is the maximum kinetic energy of the ejected electrons,
- ( h ) is Planck's constant ((6.626 \times 10^{-34} ) J·s),
- ( \nu ) is the frequency of the incident light,
- ( \phi ) is the work function of the metal, which is the minimum energy required to remove an electron from the surface of the metal.
Formula for Stopping Potential
The stopping potential (( V_s )) can be calculated by equating the maximum kinetic energy of the ejected electrons to the electric potential energy:
[ KE_{\text{max}} = eV_s ]
where:
- ( e ) is the elementary charge ((1.602 \times 10^{-19}) C).
Rearranging the formula gives us:
[ V_s = \frac{KE_{\text{max}}}{e} = \frac{h\nu - \phi}{e} ]
Key Points and Differences
| Aspect | Description |
|---|---|
| Definition | Stopping potential is the minimum voltage required to stop the most energetic photoelectrons. |
| Relation to Photoelectric Effect | Directly related; it is a measure of the energy of photoelectrons due to incident light. |
| Dependency | Depends on the frequency of the incident light and the work function of the metal. |
| Units | Measured in volts (V). |
| Determination | Can be experimentally determined by measuring the voltage at which photocurrent becomes zero. |
Examples
Example 1: Calculating Stopping Potential
Suppose a metal with a work function of ( 2.0 \times 10^{-19} ) J is illuminated with light of frequency ( 1.0 \times 10^{15} ) Hz. Calculate the stopping potential.
Using the formula:
[ V_s = \frac{h\nu - \phi}{e} ]
we plug in the values:
[ V_s = \frac{(6.626 \times 10^{-34} \text{ J·s})(1.0 \times 10^{15} \text{ Hz}) - (2.0 \times 10^{-19} \text{ J})}{1.602 \times 10^{-19} \text{ C}} ]
[ V_s = \frac{6.626 \times 10^{-19} \text{ J} - 2.0 \times 10^{-19} \text{ J}}{1.602 \times 10^{-19} \text{ C}} ]
[ V_s = \frac{4.626 \times 10^{-19} \text{ J}}{1.602 \times 10^{-19} \text{ C}} ]
[ V_s \approx 2.89 \text{ V} ]
Therefore, the stopping potential is approximately 2.89 volts.
Example 2: Effect of Light Frequency on Stopping Potential
If the frequency of the incident light is increased while keeping the work function constant, the stopping potential will also increase. This is because the kinetic energy of the ejected electrons is directly proportional to the frequency of the incident light.
For instance, if the frequency is doubled, the stopping potential will also increase, assuming the work function remains unchanged.
Conclusion
The stopping potential is a critical concept in understanding the photoelectric effect and the behavior of electrons when exposed to light. It provides a quantitative measure of the energy of photoelectrons and is influenced by the frequency of the incident light and the work function of the metal. By studying the stopping potential, physicists can gain insights into the properties of materials and the nature of light-matter interactions.