Photoelectric Effect, Work Function, Threshold Frequency, Wavelength, Speed & Kinetic Energy, Electr
Summary
TLDRThis 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
🌟 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.
🔍 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.
🚀 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.
🌈 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.
📚 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.
Mindmap
Keywords
💡Photoelectric Effect
💡Threshold Frequency
💡Wavelength
💡Frequency
💡Work Function
💡Planck's Constant
💡Intensity
💡Kinetic Energy
💡Electron Volt (eV)
💡Speed of Light
💡Avogadro's Number
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
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