Photoelectric Effect, Work Function, Threshold Frequency, Wavelength, Speed & Kinetic Energy, Electr

Summary

This educational video delves into the photoelectric effect, explaining how light of a certain frequency can eject electrons from a metal surface. It covers the concept of threshold frequency, the work function, and how to calculate it using Planck's constant. The script provides step-by-step solutions for determining the kinetic energy and speed of ejected electrons, using given wavelengths and work functions of different metals. It also demonstrates conversions between electron volts and joules, and calculates maximum wavelengths for electron ejection from potassium and calcium metals.

Takeaways

• 🌞 The photoelectric effect occurs when light of a certain frequency shines on a metal, causing electrons to be ejected if the light's energy matches or exceeds the metal's work function.
• 🔍 Light with a lower frequency, such as red light, generally doesn't have enough energy to eject electrons from a metal surface, regardless of its intensity.
• 🔵 Higher frequency light, like blue light, can eject electrons from a metal surface, and increasing its intensity can lead to more electrons being ejected.
• ⚡ The work function (W) of a metal is the minimum energy required to remove an electron from the metal's surface and can be calculated using Planck's constant (h) and the threshold frequency (ν₀).
• 📐 The threshold frequency can be found using the formula W = h * ν₀, where W is given and h is Planck's constant.
• 🚀 The kinetic energy of an ejected electron is the difference between the energy of the incident photon and the work function of the metal.
• 📐 The energy of a photon can be calculated using the formula E_photon = h * c / λ, where c is the speed of light and λ is the wavelength of the light.
• 🌈 The speed of an ejected electron can be determined using the kinetic energy and the mass of the electron with the formula KE = 1/2 * m * v².
• 🌌 The maximum wavelength of light that can free an electron from a metal can be found by rearranging the work function equation to solve for wavelength.
• 🔋 The work function of a metal can also be expressed in electron volts (eV), where 1 eV equals 1.6 × 10⁻¹⁹ joules.
• 🛠 To find the speed of an electron, use the kinetic energy formula and solve for velocity, considering the mass of the electron in kilograms.

Q & A

What is the photoelectric effect?

The photoelectric effect is a phenomenon where electrons are ejected from a metal surface when it is exposed to light of a certain frequency. If the light's frequency is high enough, the energy of the photons can be transferred to the electrons, giving them enough kinetic energy to escape from the metal's atoms.

Why does the frequency of light matter in the photoelectric effect?

The frequency of light determines whether the photons have enough energy to eject electrons from the metal. If the frequency is too low, even if the light's intensity is high, the electrons will not be ejected because each photon does not carry enough energy.

What is the relationship between light intensity and the number of ejected electrons?

Once the threshold frequency is surpassed, increasing the light's intensity can increase the number of photons, which in turn can eject more electrons from the metal surface. However, if the threshold frequency is not met, increasing intensity will not affect electron ejection.

What is the work function in the context of the photoelectric effect?

The work function, often denoted as Φ (Phi), is the minimum energy required to remove an electron from a metal surface. It is typically given in joules and can be calculated using Planck's constant and the threshold frequency.

How can you calculate the threshold frequency of a metal given its work function?

The threshold frequency can be calculated using the formula for the work function: Φ = h × (threshold frequency), where h is Planck's constant. By rearranging the formula, you can solve for the threshold frequency: threshold frequency = Φ / h.

What is the kinetic energy of an ejected electron?

The kinetic energy of an ejected electron is the difference between the energy of the incident photon and the work function required to eject the electron. If the photon's energy is greater than the work function, the excess energy becomes the electron's kinetic energy.

How do you find the speed of an electron using its kinetic energy?

The speed of an electron can be found using the kinetic energy formula: KE = 0.5 × m × v^2, where KE is the kinetic energy, m is the mass of the electron, and v is the speed. By rearranging the formula and solving for v, you can find the electron's speed.

What is the maximum wavelength of light that can free an electron from potassium metal?

The maximum wavelength can be found by rearranging the work function formula to solve for wavelength: wavelength = (h × c) / Φ, where h is Planck's constant, c is the speed of light, and Φ is the work function in joules. For potassium, with a work function of 2.3 eV, the maximum wavelength is approximately 540 nm.

How can you convert the work function from kilojoules per mole to electron volts?

To convert the work function from kilojoules per mole to electron volts, first convert kilojoules to joules by multiplying by 1000, then divide by Avogadro's number to get the energy per photon in joules, and finally divide by 1.6 × 10^-19 joules to convert to electron volts.

What is the significance of Avogadro's number in converting work function to electron volts?

Avogadro's number is used to convert the work function from a bulk scale (per mole) to an individual scale (per photon). Since one mole of any substance contains Avogadro's number of entities, dividing the work function per mole by this number gives the work function per individual photon.

How does the color of light relate to its ability to eject electrons in the photoelectric effect?

The color of light is related to its frequency, with blue light having a higher frequency than red light. Higher frequency light, such as blue or violet, has enough energy to eject electrons from certain metals, while lower frequency light, like red, usually does not.

Outlines

00:00

🌟 Understanding the Photoelectric Effect

This paragraph introduces the photoelectric effect, explaining how light of a certain frequency can eject electrons from a metal surface. It emphasizes the necessity of light having a high enough frequency to overcome the metal's threshold frequency and the irrelevance of light intensity if the frequency is insufficient. The paragraph uses the example of red and blue light to illustrate the concept and introduces the equation relating work function, Planck's constant, and threshold frequency to calculate the minimum frequency required to eject electrons.

05:01

🔍 Calculating Threshold Frequency and Electron Kinetic Energy

The second paragraph delves into the calculation of the threshold frequency using the work function and Planck's constant, providing a numerical example with a metal having a work function of 3.06 x 10^-19 joules. It then explains how to calculate the kinetic energy of the ejected electrons, using the difference between the photon's energy and the work function. The process involves using the speed of light, wavelength, and Planck's constant to find the photon's energy and then subtracting the work function to determine the kinetic energy of the electrons.

10:02

🚀 Determining Electron Speed and Maximum Wavelength for Potassium

This section discusses how to find the speed of an electron using its kinetic energy and the electron's mass. It provides a step-by-step calculation for the speed of an electron ejected from a metal surface when illuminated with light of a specific wavelength. The paragraph also addresses how to calculate the maximum wavelength of light required to free an electron from potassium metal, using the work function in electron volts, converting it to joules, and applying the relevant equations to find the threshold wavelength.

15:02

🌈 Exploring the Photoelectric Effect with Calcium Metal

The fourth paragraph extends the discussion to calcium metal, starting with the work function in kilojoules per mole and converting it to electron volts per photon. It explains the process of using Avogadro's number to relate molar work function to the energy per photon and then calculates the maximum wavelength of light that can free an electron from the surface of calcium metal. The explanation includes converting units and applying the equation involving Planck's constant and the speed of light.

20:03

📚 Comprehensive Analysis of Photoelectric Effect Calculations

The final paragraph wraps up the video script with a comprehensive analysis of the photoelectric effect calculations for various metals, including the determination of the maximum wavelength for electron ejection and the calculation of electron kinetic energy and speed. It highlights the importance of understanding the relationship between light wavelength, frequency, and the work function of different metals to predict the outcomes of photoelectric interactions.

Keywords

💡Photoelectric Effect

The photoelectric effect is a phenomenon where electrons are ejected from a metal surface when it is exposed to light of sufficient frequency. It's central to the video's theme as it explains the basic principle behind the effect and how it can be observed in different light conditions. In the script, the photoelectric effect is used to illustrate the relationship between light frequency and the ejection of electrons from a metal surface.

💡Threshold Frequency

Threshold frequency is the minimum frequency of light required to cause the photoelectric effect. It is a key concept in the video as it determines whether electrons will be ejected from a metal surface. The script explains that if the light's frequency is below this threshold, no electrons will be ejected regardless of the light's intensity.

💡Wavelength

Wavelength is the distance between two consecutive points in a wave that are in the same phase. The video discusses how the wavelength of light affects the photoelectric effect, with shorter wavelengths (such as blue light) having higher frequencies and being more effective at ejecting electrons compared to longer wavelengths (such as red light).

💡Frequency

Frequency refers to the number of cycles a wave completes in a second and is directly related to the energy of the light. In the context of the video, frequency is essential in determining the ability of light to eject electrons from a metal surface, with higher frequencies being more effective.

💡Work Function

The work function is the minimum energy required to remove an electron from a material. It is a critical concept in the video as it is used to calculate the threshold frequency and to determine the kinetic energy of ejected electrons. The script provides examples of calculating the threshold frequency using the work function of different metals.

💡Planck's Constant

Planck's constant is a fundamental physical constant that relates the energy of a photon to its frequency. The video script uses Planck's constant in equations to calculate the threshold frequency and the energy of photons, which is essential for understanding the photoelectric effect.

💡Intensity

Intensity refers to the amount of light energy striking a unit area. The video explains that while increasing the intensity of light can increase the number of electrons ejected if the threshold frequency is surpassed, it has no effect if the frequency is below the threshold.

💡Kinetic Energy

Kinetic energy is the energy that a body possesses due to its motion. In the video, the kinetic energy of ejected electrons is calculated based on the energy of the incident photons and the work function of the metal. It illustrates how the energy of light is converted into the motion of electrons.

💡Electron Volt (eV)

An electron volt is a unit of energy that is equal to the amount of kinetic energy gained or lost by an electron when it passes through an electric potential difference of one volt. The script uses electron volts to express the work function and kinetic energy of electrons, providing a standardized measure in the context of the photoelectric effect.

💡Speed of Light

The speed of light is a universal physical constant that represents the speed at which light propagates through a vacuum. The video uses the speed of light in equations to relate the frequency and wavelength of light to the photoelectric effect, showing how these properties determine the effect's occurrence.

💡Avogadro's Number

Avogadro's number is the number of constituent particles (usually atoms or molecules) in one mole of a substance. The video mentions Avogadro's number in the context of converting the work function from kilojoules per mole to the energy per photon, which is necessary for understanding the energy requirements for the photoelectric effect at the atomic level.

Highlights

Introduction to the photoelectric effect and its significance in chemistry.

Explanation of how electrons are ejected from a metal surface when light of the right frequency is shone on it.

The necessity of a certain light wavelength for the photoelectric effect to occur.

Example of red light's insufficient frequency to eject electrons from metals.

Blue light's higher frequency and its ability to eject electrons compared to red light.

Concept of threshold frequency for electron ejection.

The relationship between light intensity and the number of ejected electrons.

Calculation of threshold frequency using Planck's constant and work function.

Illustration of how to calculate the kinetic energy of ejected electrons.

Use of the speed of light and wavelength to determine photon energy.

Derivation of the equation to calculate the kinetic energy of electrons from given wavelength.

Conversion of electron's kinetic energy from joules to electron volts.

Explanation of how to find the maximum wavelength needed to free an electron from a metal surface.

Conversion of work function from kilojoules per mole to electron volts.

Calculation of the maximum wavelength for electron ejection from calcium metal.

Understanding the practical implications of the photoelectric effect on different metals and light wavelengths.

Final summary of the photoelectric effect principles and calculations covered in the video.

Transcripts

in this video we're going to focus on

the photoelectric effects and how to

solve chemistry problems associated with

it

so what is the photoelectric effect

so let's say if we have a metal

and if we shine light on its metal

if it has the right frequency

the electrons in this metal can be

ejected off the surface

so the energy that's carried by a photon

can be transferred to an electron

given enough kinetic energy to escape

from the atoms of the metal

and so that's the basic idea behind the

photoelectric effect

now

this light

has to be of a certain wavelength

if the frequency is not high enough

the electrons will not be ejected off

the surface of the metal

now i'm going to use red light as an

example because red light has a

relatively low frequency compared to

blue light

so for most metals if you shine it

with red light

it's not going to be enough red light

doesn't have

enough frequency or enough energy to

eject an electron

from the surface of this metal

so it doesn't matter if you increase the

intensity

of the red light so if you shine more

red light photons on this metal no

electrons will be ejected off this metal

now let's say if you shine

blue light which has a much higher

frequency than red light

on its metal

then electrons will be ejected off the

surface of the metal

now if you increase the intensity of the

blue light let's say if you

add more photons

on this metal surface

more electrons will be ejected

off the surface

so there is a threshold frequency a

minimum frequency at which electrons

will be ejected

once you surpass that frequency

if you increase the intensity

then you can increase the number of

electrons

that will leave the surface

but if you don't pass that threshold

frequency

increasing the intensity will have no

effect

on ejecting the electrons

so now looking at this problem

it says that a certain metal has a work

function

of 3.06 times 10 to the negative 19

joules

and light with a wavelength of 450

nanometers

shines on the surface of the metal

what is the threshold frequency

so what equation can we use

to calculate the threshold frequency

the work function

in chemistry you might see it as e

naught

is equal to

planck's constant times the threshold

frequency

you can use w for the work function if

you want to

because

w corresponds with work

but i'm going to use this equation now

so we're given a work function which is

3.06

times 10 to the negative 19 joules

and planck's constant which is h

that's equal to 6.626

times 10 to the minus 34.

and so we can calculate the frequency

so the frequency

it's simply

the energy divided by planck's constant

so it's 3.06 times

10 to the negative 19 joules

divided by 6.626

times 10 to the minus 34.

so the threshold frequency in this

problem is

4.62 times 10 to the 14 hertz

so unless you shine light with a

frequency that's equal to or greater

than this number

no electrons will be ejected

off the surface of this metal

so the frequency has to be equal to this

number or higher if it's less than its

number the electrons are not going to

leave the metal they're going to just

stay on it

now let's move on to part b calculate

the kinetic energy of the ejected

electron

so how can we find that

the kinetic

of the ejected electron

is equal

to the energy of the photon

minus

the energy that's required

to eject the electron

so let's just use some numbers for

example

let's say

just for the sake of illustrative

purposes

that it takes

200 joules of energy

to release the electron

and let's say if we

shine 300 joules of light energy on this

metal

then if 200 is used to free the electron

the remaining 100

is the kinetic energy of the electron

that's how much energy it has left over

to

move away from

the metal

so the difference

between the energy of the photon and the

energy that's required to free the

electron that difference is the kinetic

energy of the electron

and so the greater the difference the

more speed that the electron will have

as it leaves the metal surface

now the energy of the photon

is basically planck's constant

times the actual frequency

of the photon

minus

the work function

which is planck's constant times the

threshold frequency

now

we don't have the frequency of the

photon we have the wavelength so we need

to adjust the equation

if you recall the speed of light is

equal to the wavelength times the

frequency

so the frequency is the speed of light

divided by the wavelength

so what i'm going to do is i'm going to

replace the frequency with

this term

so the energy of the photon can also be

expressed using this equation it's

planck's constant times the speed of

light divided by the wavelength

minus

this thing which we already have it in

joules so i'm going to leave the work

function as enough

so this is the equation that we need to

calculate the kinetic energy

of the electron that's released

if we're given the wavelength of light

that shines on it

so it's going to be planck's constant

multiplied by

the speed of light

divided by the wavelength which

we need to put this in nanometers

a nanometer is 10 to the minus 9 meters

so you can write it as 450

times 10 to the negative 9 meters

so this right here will give us the

energy of the photon

minus the work function

which

we already know it to be 3.06

times 10 to the negative 19 joules

so go ahead and plug in these values

into your calculator

so the answer that i have

is 1.357

times 10

to the negative 19 joules

so that's the kinetic energy

of the electron after

it's released

from the metal

now let's move on to part c what is the

speed

of this electron

to find the speed we need to use this

equation the kinetic energy of an

electron

is one-half mv squared

so we have the kinetic energy is 1.357

times 10 to the negative 19 joules

and the mass of an electron which has to

be in kilograms and not grams

it's 9.11

times 10 to the minus 31 kilograms

so what we need to do is take 1.357

times 10 to the minus 19

divided by 0.5

and then take that result divided by

9.11 times 10 to the minus 31.

so you should get 2.979

times 10 to 11 which is equal to the

square of the speed

so now to calculate the speed take the

square root of both sides

so the speed

of the electron

is going to be

545

815 meters per second

or you can write it as

5.46 times

10 to the 5 meters per second

so that's the speed of the electron

number two

the work function of potassium metal

is 2.3 electron volts

what is the maximum wavelength of light

that is needed to free an electron from

the surface of potassium metal

so how can we find the answer

well we know that the work function

is equal to

planck's constant times the threshold

frequency

and we know that the frequency is the

speed of light divided by the wavelength

so the work function is equal to

planck's constant

times the speed of light

divided by the maximum wavelength

now let's rearrange the equation to

calculate the maximum wavelength

so what i'm going to do is multiply both

sides

by

the maximum wavelength divided by the

work function

so on the left side

these two will cancel and on the right

side

the wavelength will cancel

so the maximum wavelength

is planck's constant times the speed of

light

divided by

the work function

of potassium metal

now we need to get the work function

in joules right now we have it in

electron volts

so how do we convert electron volts to

joules

so let's start with 2.3 electron volts

you need to know that one electron volt

is equal to 1.6 times 10

to the minus 19 joules

so this will give you a work function of

3.68

times 10 to the negative 19 joules

so now we can plug it into the equation

so we have planck's constant

which is in joules time seconds

multiplied by the speed of light

which is meters per second

divided by the energy

or the work function in joules

so notice that the unit

joules cancel

and seconds cancel as well

giving us the wavelength in meters

so you should get

5.40

times ten to the minus seven

meters

now let's convert the wavelength

from meters to nanometers because it's

typically reported

in nanometers with these kinds of

questions

so let's start with this value

and keep in mind that

one nanometer

is

1 times 10 to the minus 9

meters

so what you could do is take this value

move it to the top

and by doing that the negative 9 changes

to positive 9. so this is 5.4

times 10 to the minus 7

times 10 to the positive 9

nanometers so negative 7 plus 9 is

positive 2.

so this becomes 5.4

times 10 squared nanometers and 10

squared 10 times 10 is 100

so 5.4 times 100 is 540.

so the wavelength

or rather

the maximum wavelength that is needed to

free an electron

from the surface of potassium metal is

540 nanometers

anything less than this number will be

enough to free an electron

so if we shine let's say light with red

light with

670

nanometers

red light won't be strong enough to

knock off an electron from the surface

of potassium metal but let's say if we

shine blue light on it with a wavelength

of 480 nanometers

that should be enough or it will be

enough

to remove an electron from potassium

metal

so as you can see red light

usually doesn't have enough energy

to knock off an electron from a metal

surface

but blue light can for certain metals

now let's move on to part b

if light

with a wavelength of 425 nanometers

shines on this model

what will be the kinetic energy of this

electron

in electron volts

so around

425

you're dealing with purple light

and that's definitely high enough to

remove an electron

now if you want to calculate the kinetic

energy

given the wavelength of the

electromagnetic radiation that's on it

it's going to be planck's constant times

the speed of light divided by that

wavelength

minus

the work function of the metal

so it's going to be this number again

times

the speed of light which is 3 times 10

to the 8

meters per second

divided by

the wavelength which is 425

times 10 to the minus 9 meters

so don't forget to convert nanometers to

meters

now the work function has to be in

joules

not electron volts

so if you recall to convert electron

volts to joules

take the 2.3 and multiply by 1.6 times

10

to the negative 19.

and so that's 3.68

times 10 to the negative 19 joules

so let's plug this stuff in

so you should get 9.97

times

10 to the negative 20 joules

so that's the kinetic energy

of the electron

after its release but now let's convert

it to electron volts

so all we need to do is just divide it

by 1.6 times 10 to the negative 19

joules

and so the kinetic energy in electron

volts

is 0.623

ev

now let's move on to part c

calculate the speed of this electron

so to do that

we need to use this equation kinetic

energy is equal to one-half

mv squared

but make sure you use the kinetic energy

value that's in joules

so replace ke with 9.97

times 10 to the negative 20 joules

you don't want to use the kinetic energy

value in electron volts

now the mass of the electron is the same

as the last problem

9.11 times 10 to the minus 31 kilograms

so just like before we're going to take

the kinetic energy 9.97

times 10 to the minus 20 and then divide

it by 0.5

and then divide that by 9.11

times 10 to the minus 31.

so you should get 2.188

times 10 to 11 and then take the square

root of that number

and so the speed

that i have is 467 000 eight hundred

forty six point five meters per second

which we can round and say it's about

four point six eight

times ten to the five

meters per second

so as you can see these electrons are

moving very fast

now let's move on to our last question

the work function of calcium metal is

276.5 kilojoules per mole

what is the work function in electron

volts

so one mole

of calcium atoms

has a work function of

276.5 kilojoules

now every calcium atom

requires a single photon to knock off

one electron

so therefore one mole of calcium atoms

requires

one more of photons

it's a one-to-one ratio

now what do you think we need to do next

the next thing that we need to do

is use avogadro's number

so one mole of photons

corresponds

to 6.022

times 10 to the 23 photons

so now we can cancel these units

now we need to convert kilojoules to

joules

one kilojoule

is equal to a thousand joules

so now that we have

the unit joules per photon

we can convert joules to electron volts

one electron volt

is 1.6 times 10

to the negative 19 joules

so now what we have is the electron volt

per photon

which is what we want

so it's 276.5

divided by avogadro's number

multiplied by a thousand

divided by 1.6 times 10 to negative 19.

so it's 2.87

electron volts

per single photon

so that's the energy of one photon

so that's the minimum energy that's

needed to knock off a single electron so

the work function of calcium metal is

2.87 electron volts

now what is the maximum wavelength of

light that is needed to free an electron

from the calcium metal surface

so to find that maximum wavelength we

know it's planck's constant times the

speed of light

divided by the work function

in joules

so we have the work function in joules

if

we stop the conversion

here

because this gives us the work function

in electron volts but if we want it in

joules

we need to basically get rid of this

part

so this is going to be planck's constant

times the speed of light

and the work function in joules is going

to be 276.5

divided by avogadro's number

times a thousand

so the work function is 4.59

times 10 to the negative 19 joules

so the maximum wavelength is

4.33 times 10 to the 7 meters

which is

equivalent to 433 nanometers

and so that's the answer

you