Work function
ϕ
=
4
eV
ϕ=4eV.
Light wavelength
λ
=
300
nm
λ=300 nm incident.
Find maximum kinetic energy (in eV) of emitted photoelectrons.
视频信息
答案文本
视频字幕
The photoelectric effect is a quantum mechanical phenomenon where photons of light strike a metal surface and cause the emission of electrons. In this problem, we have a metal with work function phi equals 4 electron volts, and incident light with wavelength 300 nanometers. The work function represents the minimum energy needed to remove an electron from the metal surface.
Einstein's photoelectric equation states that the maximum kinetic energy of emitted photoelectrons equals the photon energy minus the work function. The photon energy is given by h f, where h is Planck's constant and f is the frequency. We can also express photon energy as h c over lambda, relating energy to wavelength. This equation shows energy conservation: the incoming photon energy is either used to overcome the work function or becomes kinetic energy of the electron.
To find the photon energy, we use the relationship E equals h c over lambda. Substituting our known values: h equals 4.136 times 10 to the minus 15 electron volt seconds, c equals 3 times 10 to the 8 meters per second, and lambda equals 300 nanometers or 300 times 10 to the minus 9 meters. Calculating step by step: E equals 4.136 times 10 to the minus 15, times 3 times 10 to the 8, divided by 300 times 10 to the minus 9. This gives us 4.136 electron volts for the photon energy.
Now we apply Einstein's photoelectric equation to find the maximum kinetic energy. KE max equals E photon minus phi. Substituting our calculated photon energy of 4.136 electron volts and the given work function of 4 electron volts: KE max equals 4.136 minus 4, which equals 0.136 electron volts. This energy diagram shows that most of the photon energy goes into overcoming the work function, leaving only a small amount as kinetic energy for the emitted photoelectrons.
We have a photoelectric effect problem. Light with wavelength 300 nanometers strikes a metal surface with work function 4 electron volts. We need to find the maximum kinetic energy of the emitted photoelectrons.
The photoelectric effect is described by Einstein's equation: maximum kinetic energy equals photon energy minus work function. We need the Planck constant, speed of light, and can calculate frequency from wavelength.
First, we calculate the frequency using c equals lambda f. Then we find the photon energy using Planck's equation E equals h f. Finally, we convert from joules to electron volts using the elementary charge.
Now we apply Einstein's equation. The maximum kinetic energy equals photon energy minus work function: 4.136 minus 4.000 equals 0.136 electron volts. We verify that photon energy exceeds the work function, so photoelectric emission does occur.
Our result of 0.136 electron volts has clear physical meaning. The photon energy only slightly exceeds the work function, resulting in near-threshold emission. The emitted photoelectrons have low kinetic energy, demonstrating the quantum nature of light and the threshold behavior that classical physics could not explain.