What happens when light strikes the surface of a metal? The **Photoelectric Effect **can help to explain that.

Examining the Photoelectric Effect

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concept

## Photoelectric Effect

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now, Einstein theorized that if a photon met an energy requirement and struck a metal surface, then electrons could be ejected. This is known as the photo electric effect. So here, if we look at it, we have a metal surface here, and on this metal surface, we have free flowing electrons in green. Now we're going to say that to this metal surface. I'm going to strike it with some form of energy here represented by energy of a photon. If it hits the surface with enough energy and enough force, it can dislodge one of these electrons. That electron can then convert that energy excess energy into kinetic energy and propel itself further away from the metal surface. So this is what we call our kinetic energy. Now, for this to happen, we have to realize that when the energy of the photons or light source is greater, then the energy of the surface, which we're gonna abbreviated as B e. Then we can inject an electron. But if the energy the light source is not greater than the energy off the surface of the metal, then electron will not be ejected from that metal service, and it will stay there. So this is basically the idea when it comes to the photo electric effect. Now let's click on to the next video and go a little bit more in detail about what exactly is energy K e versus energy be?

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concept

## Photoelectric Effect

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so we know that if enough energy is bombarded on the metal surface, it'll kick in. Electron off. Now we use the brief abbreviation be this stands for binding energy here. This is the minimum amount of energy needed to inject an electron from a metal surface. We're gonna say it's also known as our threshold frequency or our work function of the metal. So it goes by a lot of different names. So binding energy, threshold frequency as well as work function now kinetic energy. We say that this is the energy and elect object has due to its speed or motion. So basically any excess energy that the electron games from this light source will be converted into kinetic energy. Now, from this, we can say that the photo electric formula photo electric effect formula is total energy, which is the photon equals the binding energy, plus your kinetic energy, which we say is your surplus energy. So when we're dealing with any type of photo electric question that requires some type of calculation, it usually deals with this formula. So total energy equals binding energy plus kinetic energy

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example

## Photoelectric Effect Example 1

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here, we're told that the binding energy of electrons on a metal surface are 7. times 10 to the negative 19 jewels. If an outside energy source with 4.33 times 10 to negative jewels strikes the metal surface, what would be the kinetic energy of an electron Ejected electron. So just remember that your total energy, which is the photon, equals the binding energy plus your kinetic energy. The total energy of the photon comes from this outside energy source. So that's 4.33 times 10 to the negative. 17 jewels equals you're binding energy, which is 7.15 times 10 to the negative. 19 jewels plus the kinetic energy of the electron ejected. So subtract out 7.15 times 10 to the negative jewels from both sides. So when we do that, we're gonna get left the kinetic energy of the ejected electron. So the kinetic energy here equals 4.26 times 10 to the negative 17 jewels. So this would be the energy kinetic energy Energy of motion for that ejected electron

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concept

## Photoelectric Effect

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now the photo electric effect formula can be expanded when we're given the additional variables of mass and velocity. So here we're going to say with the new expanded formula that the energy of a photon can be seen as energy of a photon equals your binding energy plus your kinetic energy. And when it comes to buying the energy of a photon, we're gonna say it's equal to Planck's constant, which is H. Times your frequency which is mu binding energy. Remember is just abbreviated as B. E. And your kinetic energy energy of motion equals a half times the mass of the electron. In this case times velocity squared. Now sometimes you'll see instead of jewels or killer jewels being used, we might see E. V. Which stands for electron volts. So just remember here that one electron volt equals 1.602 times 10 to the negative 19 jewels. So just remember if energy is given in electron volts, then use the conversion factor to change it into jewels. Okay, so with our new expanded formula, we could substitute this in for the energy of a photon and we could substitute this in for the kinetic energy of the ejected electron

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example

## Photoelectric Effect Example 2

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here. It says what? The surface of the metal exposed of photons at a frequency of 7.13 times to the 16 seconds inverse electrons air admitted with a maximum kinetic energy of 6.30 times 10 to the negative 19 jewels. Here, we need to calculate the work function off the metal. Alright, So first of all, remember, work function is another name for binding energy or threshold frequency. So this is E. Now, remember, we're gonna say the energy total energy of our photon equals binding energy or, in this case, work function, plus kinetic energy in terms of energy of a photon that equals plank's constant times your frequency. So using that frequency given to us initially will help us to figure out the total energy of our photon. So here those plank's constant plug in your frequency. Okay, so when we do that, we're gonna get our energy of our photon as 4.7243 times 10 to the negative 17 jewels. So take that and plug it in okay for three times 10 to the negative 17 jewels binding energy. Or, in this case, work function is what we're looking for. And they give us the kinetic energy as 6.30 times 10 to the negative 19 jewels. Subtract that out from both sides and we'll have our work function at the end. So then here, when we take that and plug it in, we're gonna have our binding energy or our work function as equaling 4.66 times 10 to the negative jewels as our final answer for our

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Problem

A metal with a threshold frequency of 2.15 x 10^{1}^{5} s^{-1} emits an electron with a velocity of 7.03 x 10^{6} m/s when radiation of 1.88 x 10^{15} s^{-1} strikes the metal’s surface. Calculate the mass of the electron.

A

6.97 x 10

^{-22}kgB

4.98 x 10

^{-21}kgC

2.96 x 10

^{-21}kgD

8.11 x 10

^{-22}kg7

Problem

An ultraviolet photon with a wavelength of 320 nm strikes a metal surface. The emitted electron has a kinetic energy of 1030 eV. What is the binding energy of the electron in kJ/mol? 1 electron volt (eV) = 1.602 x 10^{-19} J.

A

5.98 x 10

^{35}kJ/molB

5.65 x 10

^{35}kJ/molC

6.55 x 10

^{34}kJ/molD

4.56 x 10

^{35}kJ/molAdditional resources for Photoelectric Effect

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