Photons with a wavelength of 400 nm are incident on an unknown metal and electrons are ejected

Photons with a wavelength of 400 nm are incident on an...

Photons with a wavelength of $400 \mathrm{~nm}$ are incident on an unknown metal and electrons are ejected from the metal. However, when photons with a wavelength of $700 \mathrm{~nm}$ are incident on the metal, no electrons are ejected. (a) Could this metal be cesium with a work function of $1.8 \mathrm{eV} ?$ (b) Could this metal be tungsten with a work function of $4.6 \mathrm{eV} ?$ (c) Calculate the maximum kinetic energy of the ejected electrons for each possible metal when $200-\mathrm{nm}$ photons are incident on it.

Key Concepts

Kinetic Energy of Emitted Electrons

Once an electron is ejected, its maximum kinetic energy is given by the difference between the photon energy and the work function, expressed as K_max = hf - ?. This concept is crucial for understanding the energy balance in the photoelectric effect and how variations in photon energy translate to changes in the kinetic energy of emitted electrons.

Threshold Frequency

The threshold frequency is the minimum frequency that photons must have to provide enough energy to free electrons from a material. It is derived from the work function, and any photon with a frequency lower than this threshold will not cause electron emission irrespective of the light's intensity.

Photon Energy and Frequency

Photon energy is directly proportional to its frequency, as described by the equation E = hf, where h is Planck's constant and f is the frequency of the photon. This relationship is fundamental to determining whether an incident photon has sufficient energy to overcome the work function and initiate 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 an intrinsic property of the material that sets the threshold for photoelectron emission. Only incident photons that possess energy above this value can liberate electrons from the material.

Photoelectric Effect

The photoelectric effect is the process by which electrons are emitted from a material after the absorption of incident light. It demonstrates the particle nature of light, emphasizing that light consists of discrete packets of energy called photons. In this process, only photons with energy greater than or equal to the material’s work function can eject electrons.

Transcript

00:01 In this exercise, we have photons shining on a metal, and we have the information that for the wavelength of 400 nanometers, the photon can remove electrons from the metal, but with a wavelength of 700 nanometers, the photons cannot remove any electrons.

00:20 So for question a, we are asked if this metal could be cesium that has a work function of, 1 .8 electron volts.

00:34 So the first thing we need to notice is that since 400 nanometers photons remove electrons and 700 nanometers do not, the cutoff wavelength for this matter is between 400 nanometers.

00:54 Lambda c is the cutoff wavelength.

00:57 It's between 400 nanometers and 700 nanometers.

01:01 And the cutoff wavelength is the maximum wavelength that the photons can have so that they expel electrons from the metal.

01:10 We also know that the minimum energy that the photons photons will have to have in order to remove electrons from a metal is equal to the work function and the energy of a photon is given by hc over lambda.

01:26 So from this we can calculate what is the cutoff frequency, okay, the maximum frequency, isolating lambda c in this formula.

01:39 So you're going i have hc over phi.

01:43 So let's calculate the cutoff frequency for the cesium and see if it lies in this range that we've established here.

01:52 Hc is 1 ,140 that's in electron volts nanometers.

01:59 Phi is 1 .8 electron volts so that the cutoff frequency will be 689 nanometer, cutoff, length, i'm sorry.

02:14 It's going to be 689 nanometers...

Please give Ace some feedback