# 29.2 The photoelectric effect  (Page 4/8)

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## Phet explorations: photoelectric effect

See how light knocks electrons off a metal target, and recreate the experiment that spawned the field of quantum mechanics.

## Section summary

• The photoelectric effect is the process in which EM radiation ejects electrons from a material.
• Einstein proposed photons to be quanta of EM radiation having energy $E=\text{hf}$ , where $f$ is the frequency of the radiation.
• All EM radiation is composed of photons. As Einstein explained, all characteristics of the photoelectric effect are due to the interaction of individual photons with individual electrons.
• The maximum kinetic energy ${\text{KE}}_{e}$ of ejected electrons (photoelectrons) is given by ${\text{KE}}_{e}=\text{hf}\text{– BE}$ , where $\text{hf}$ is the photon energy and BE is the binding energy (or work function) of the electron to the particular material.

## Conceptual questions

Is visible light the only type of EM radiation that can cause the photoelectric effect?

Which aspects of the photoelectric effect cannot be explained without photons? Which can be explained without photons? Are the latter inconsistent with the existence of photons?

Is the photoelectric effect a direct consequence of the wave character of EM radiation or of the particle character of EM radiation? Explain briefly.

Insulators (nonmetals) have a higher BE than metals, and it is more difficult for photons to eject electrons from insulators. Discuss how this relates to the free charges in metals that make them good conductors.

If you pick up and shake a piece of metal that has electrons in it free to move as a current, no electrons fall out. Yet if you heat the metal, electrons can be boiled off. Explain both of these facts as they relate to the amount and distribution of energy involved with shaking the object as compared with heating it.

## Problems&Exercises

What is the longest-wavelength EM radiation that can eject a photoelectron from silver, given that the binding energy is 4.73 eV? Is this in the visible range?

263 nm

Find the longest-wavelength photon that can eject an electron from potassium, given that the binding energy is 2.24 eV. Is this visible EM radiation?

What is the binding energy in eV of electrons in magnesium, if the longest-wavelength photon that can eject electrons is 337 nm?

3.69 eV

Calculate the binding energy in eV of electrons in aluminum, if the longest-wavelength photon that can eject them is 304 nm.

What is the maximum kinetic energy in eV of electrons ejected from sodium metal by 450-nm EM radiation, given that the binding energy is 2.28 eV?

0.483 eV

UV radiation having a wavelength of 120 nm falls on gold metal, to which electrons are bound by 4.82 eV. What is the maximum kinetic energy of the ejected photoelectrons?

Violet light of wavelength 400 nm ejects electrons with a maximum kinetic energy of 0.860 eV from sodium metal. What is the binding energy of electrons to sodium metal?

2.25 eV

UV radiation having a 300-nm wavelength falls on uranium metal, ejecting 0.500-eV electrons. What is the binding energy of electrons to uranium metal?

What is the wavelength of EM radiation that ejects 2.00-eV electrons from calcium metal, given that the binding energy is 2.71 eV? What type of EM radiation is this?

(a) 264 nm

(b) Ultraviolet

Find the wavelength of photons that eject 0.100-eV electrons from potassium, given that the binding energy is 2.24 eV. Are these photons visible?

What is the maximum velocity of electrons ejected from a material by 80-nm photons, if they are bound to the material by 4.73 eV?

$1.95×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{m/s}$

Photoelectrons from a material with a binding energy of 2.71 eV are ejected by 420-nm photons. Once ejected, how long does it take these electrons to travel 2.50 cm to a detection device?

A laser with a power output of 2.00 mW at a wavelength of 400 nm is projected onto calcium metal. (a) How many electrons per second are ejected? (b) What power is carried away by the electrons, given that the binding energy is 2.71 eV?

(a) $4.02×{\text{10}}^{\text{15}}\phantom{\rule{0.25em}{0ex}}\text{/s}$

(b) 0.256 mW

(a) Calculate the number of photoelectrons per second ejected from a 1.00-mm 2 area of sodium metal by 500-nm EM radiation having an intensity of $1\text{.}{\text{30 kW/m}}^{2}$ (the intensity of sunlight above the Earth’s atmosphere). (b) Given that the binding energy is 2.28 eV, what power is carried away by the electrons? (c) The electrons carry away less power than brought in by the photons. Where does the other power go? How can it be recovered?

Unreasonable Results

Red light having a wavelength of 700 nm is projected onto magnesium metal to which electrons are bound by 3.68 eV. (a) Use ${\text{KE}}_{e}=\text{hf}–\text{BE}$ to calculate the kinetic energy of the ejected electrons. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

(a) $–1.90 eV$

(b) Negative kinetic energy

(c) That the electrons would be knocked free.

Unreasonable Results

(a) What is the binding energy of electrons to a material from which 4.00-eV electrons are ejected by 400-nm EM radiation? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

what is temperature
temperature is the measure of degree of hotness or coldness of a body. measured in kelvin
a characteristic which tells hotness or coldness of a body
babar
Average kinetic energy of an object
Kym
average kinetic energy of the particles in an object
Kym
A measure of the quantity of heat contained in an object which arises from the average kinetic energy of the constituent particles of that object. It can be measured using thermometers. It has a unit of kelvin in the thermodynamic scale and degree Celsius in the Celsius scale.
ibrahim
Mass of air bubble in material medium is negative. why?
a car move 6m. what is the acceleration?
depends how long
Peter
What is the simplest explanation on the difference of principle, law and a theory
how did the value of gravitational constant came give me the explanation
how did the value of gravitational constant 6.67×10°-11Nm2kg-2
Varun
A steel ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.45 m. (a) Calculate its velocity just before it strikes the floor.
9.8m/s?
Sqrt(2*1.5m*9.81m/s^2)
Richard
0.5m* mate.
0.05 I meant.
Guess your solution is correct considering the ball fall from 1.5m height initially.
Sqrt(2*1.5m*9.81m/s^2)
Deepak
How can we compare different combinations of capacitors?
find the dimension of acceleration if it's unit is ms-2
lt^-2
b=-2 ,a =1
M^0 L^1T^-2
Sneha
what is botany
Masha
it is a branch of science which deal with the study of plants animals and environment
Varun
what is work
a boy moving with an initial velocity of 2m\s and finally canes to rest with a velocity of 3m\s square at times 10se calculate it acceleration
Sunday
.
Abdul
6.6 lol 😁😁
Abdul
show ur work
Sunday
Abdul
Abdul
If the boy is coming to rest then how the hell will his final velocity be 3 it'll be zero
Abdul
re-write the question
Nicolas
men i -10 isn't correct.
Stephen
using v=u + at
Stephen
1/10
Happy
ya..1/10 is very correct..
Stephen
hnn
Happy
how did the value 6.67×10°-11Nm2kg2 came tell me please
Varun
Work is the product of force and distance
Kym
physicist
Michael
what is longitudinal wave
A longitudinal wave is wave which moves parallel or along the direction of propagation.
sahil
longitudinal wave in liquid is square root of bulk of modulus by density of liquid
harishree
Is British mathematical units the same as the United States units?(like inches, cm, ext.)
We use SI units: kg, m etc but the US sometimes refer to inches etc as British units even though we no longer use them.
Richard
Thanks, just what I needed to know.
Nina
What is the advantage of a diffraction grating over a double slit in dispersing light into a spectrum?
yes.
Abdul
Yes
Albert
sure
Ajali
yeap
Sani
yesssss
bilal
hello guys
Ibitayo
when you will ask the question
Ana
bichu
is free energy possible with magnets?
joel
no
Mr.
you could construct an aparatus that might have a slightly higher 'energy profit' than energy used, but you would havw to maintain the machine, and most likely keep it in a vacuum, for no air resistance, and cool it, so chances are quite slim.
Mr.
calculate the force, p, required to just make a 6kg object move along the horizontal surface where the coefficient of friction is 0.25
Gbolahan
Albert
if a man travel 7km 30degree east of North then 10km east find the resultant displacement
11km
Dohn
disagree. Displacement is the hypotenuse length of the final position to the starting position. Find x,y components of each leg of journey to determine final position, then use final components to calculate the displacement.
Daniel
1.The giant star Betelgeuse emits radiant energy at a rate of 10exponent4 times greater than our sun, where as it surface temperature is only half (2900k) that of our sun. Estimate the radius of Betelgeuse assuming e=1, the sun's radius is s=7*10exponent8metres
2. A ceramic teapot (e=0.20) and a shiny one (e=0.10), each hold 0.25 l of at 95degrees. A. Estimate the temperature rate of heat loss from each B. Estimate the temperature drop after 30mins for each. Consider only radiation and assume the surrounding at 20degrees
James