In a photoelectric experiment using sodium, when incident...

In a photoelectric experiment using sodium, when incident light of wavelength $570 \mathrm{~nm}$ and intensity $1.0 \mathrm{~W} / \mathrm{m}^{2}$ is used, the measured stopping potential is $0.28 \mathrm{~V}$. (a) What would the stopping potential be for incident light of wavelength $400.0 \mathrm{~nm}$ and intensity 1.0 $\mathrm{W} / \mathrm{m}^{2} ?$ (b) What would the stopping potential be for incident light of wavelength $570 \mathrm{~nm}$ and intensity $2.0 \mathrm{~W} / \mathrm{m}^{2} ?(\mathrm{c})$ What is the work function of sodium?

Key Concepts

Intensity of Light

The intensity of light refers to the power per unit area carried by the electromagnetic wave and is associated with the number of photons hitting a surface per unit time. In the photoelectric effect, while the intensity affects the number of emitted electrons (and hence the current), it does not alter the energy of the individual electrons, which is determined solely by the frequency of the incident light.

Stopping Potential

The stopping potential is the minimum voltage required to reduce the kinetic energy of the fastest photoelectrons to zero, thereby stopping the photoelectric current. It is directly related to the maximum kinetic energy of the emitted electrons and serves as an experimental measure of that energy in photoelectric experiments.

Photon Energy

Photon energy, determined by the equation E = hf where h is Planck's constant and f is the frequency of the light, represents the quantum of energy carried by electromagnetic radiation. This concept is essential for understanding how varying the frequency (or wavelength) of light influences the photoelectric effect.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. It is a material-specific property and plays a crucial role in the photoelectric effect, as only photons with energy greater than or equal to the work function can cause electron ejection.

Photoelectric Effect

The photoelectric effect is the phenomenon in which electrons are emitted from a material when it is exposed to electromagnetic radiation of sufficient frequency. This process demonstrates the particle nature of light and is a key piece of evidence for quantum theory, as it cannot be fully explained by classical wave theory alone.

Einstein's Photoelectric Equation

Einstein's photoelectric equation, given by K_max = hf - ?, relates the maximum kinetic energy of ejected electrons to the energy of the incident photons (hf) minus the work function (?) of the material. This equation is fundamental in predicting the behavior of photoelectrons and establishing the quantization of light energy.

Transcript

00:01 For this exercise, we have a light of wavelength 570 nanometers and intensity of 1 watt per meter squared, incident on sodium.

00:17 And it's found that the stopping potential in this case will be 0 .28 volts.

00:28 And we have to find what would be the stopping potential if the light had a wavelength of 400 nanometers instead and the same intensity of 1 watt per meter squared.

00:50 So we know from the photoelectric formula that the kinetic and the maximum kinetic energy of the released electron is given by the energy of the photon, which is hc over lambda, minus the work function.

01:08 And the maximum kinetic energy of the electron is e, the charge of the electron, times the stopping potential v.

01:18 So with the first, these data here, the wavelength and the stopping potential that we're given to us, we can find the work function phi of the sodium.

01:31 So let's do it.

01:32 The work function phi is going to be equal to hc over lambda minus ev.

01:40 Now hc is 120 nanometers, electron volts nanometers.

01:47 Lambda is 570 nanometers.

01:52 And the e times v is going to be 0 .28 electron volts.

02:00 And this results in 1 .9 electron volts.

02:07 So this is the work function.

02:10 And now we can find the stopping potential v, again using the photoelectric equation.

02:18 So it's going to be hc over the new wavelength minus phi.

02:28 So this is going to be 1 ,240, over the new wavelength...