The photoelectric threshold wavelength of a tungsten surface is 272 nm. Calculate the maximum ki

The photoelectric threshold wavelength of a tungsten surface...

Key Concepts

Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are ejected from a material, typically a metal, when it absorbs electromagnetic radiation. This effect provided key evidence for the quantum nature of light and led to the development of quantum mechanics by showing that light can behave both as a wave and as a particle.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. It is a material-dependent property that represents the binding strength of the electrons to the material. In calculations of the photoelectric effect, the work function is used to determine the threshold energy, which is often given in terms of a threshold wavelength or frequency.

Threshold Frequency and Wavelength

The threshold frequency (or equivalently, the threshold wavelength) is the minimum frequency (or maximum wavelength) of incident light required to eject electrons from the surface of a material. Light with a frequency below this threshold will not provide enough energy to overcome the work function, and thus no electrons will be emitted.

Einstein’s Photoelectric Equation

Einstein’s photoelectric equation relates the energy of the incident photon to the work function of the material and the maximum kinetic energy of the emitted electron. The equation is given by: Energy of photon = Work function + Maximum kinetic energy. This relationship is fundamental in quantifying the kinetic energy of ejected electrons based on the incident light frequency.

Photon Energy Calculation

Photon energy can be calculated using the equation E = hf or E = hc/?, where h is Planck’s constant, f is the frequency of the radiation, c is the speed of light, and ? is the wavelength of the radiation. This calculation is essential in the context of the photoelectric effect, as it allows the determination of the energy imparted to electrons by incident photons.

Transcript

00:01 Okay.

00:02 In this problem, we are asked to find the kinetic energy of ejected photo electrons given a known threshold wavelength for our particular metal that the electrons are being ejected from.

00:17 We also know the energy of the incoming light used to eject these photo electrons.

00:23 So the main equation we're going to use to find the kinetic energy in this problem is this expression of conservation of energy.

00:30 Namely, and it'd be useful to have a diagram here to see what's happening.

00:36 Say we have light incoming with a certain energy.

00:40 The energy of light is proportional to its frequency, hf, and this, if we know that the, if this surface, this metal, has a work function fee, then we know that electrons, that if energy is incoming at an energy larger than fee, it'll eject photo electrons with a certain energy k, the kinetic energy that these photo electrons will have is simply going to be the energy of the incoming light minus this threshold energy called the work function fee.

01:14 So we know it.

01:15 So this expression depends on the frequency of the incoming light and the work function, both of which we don't directly know.

01:23 We actually can find the frequency of this light rather easily by using this formula, this expression, c equals lambda f.

01:30 In other words, c, the unchanging speed of light is equal to the product of light's wavelength and frequency, which if one increases, the other must decrease.

01:42 So this is an indirect way for us to arrive at the frequency of light given a wavelength.

01:49 In order to find the work function, we need to manipulate this equation more thoroughly.

01:55 So the two constants will need for this problem are the speed of light, of course.

01:58 Three times 10 to the 8 meters per seconds is a very good approximation.

02:02 And we're going to use the plane constant 4 .136 e to the negative 15 electron volts seconds.

02:08 Okay, so let's jump into this problem.

02:24 So first things first, we can get the frequency of our light which we'll need for later.

02:29 So using the expression c equals lambda f, we know c, it's a constant, and we know lambda threshold, this is our threshold lambda for our particular material.

02:38 So this will allow us to get a threshold frequency.

02:44 F is going to simply be, well, i should say, f, threshold is simply the speed of light divided by lambda threshold, which numerically would be e to the 8, e times 10 to the 8, rather, meters per second.

03:02 Divided by our wavelength, which is given to us to be 272, e to the negative 9 meters...

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