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A graph of frequency verses kinetic energy of an electron is shown, where frequency is along x axis and kinetic energy is along the y axis. The plot is a straight line having an inclination with x axis and meets the x axis at f sub zero, known as threshold frequency, given by B E divided by h. The threshold kinetic energy is written as equal to h f minus B E.
Photoelectric effect. A graph of the kinetic energy of an ejected electron, KE e size 12{"KE" rSub { size 8{e} } } {} , versus the frequency of EM radiation impinging on a certain material. There is a threshold frequency below which no electrons are ejected, because the individual photon interacting with an individual electron has insufficient energy to break it away. Above the threshold energy, KE e size 12{"KE" rSub { size 8{e} } } {} increases linearly with f size 12{f} {} , consistent with KE e = hf BE size 12{"KE"= ital "hf" - "BE"} {} . The slope of this line is h size 12{h} {} —the data can be used to determine Planck’s constant experimentally. Einstein gave the first successful explanation of such data by proposing the idea of photons—quanta of EM radiation.

Einstein’s idea that EM radiation is quantized was crucial to the beginnings of quantum mechanics. It is a far more general concept than its explanation of the photoelectric effect might imply. All EM radiation can also be modeled in the form of photons, and the characteristics of EM radiation are entirely consistent with this fact. (As we will see in the next section, many aspects of EM radiation, such as the hazards of ultraviolet (UV) radiation, can be explained only by photon properties.) More famous for modern relativity, Einstein planted an important seed for quantum mechanics in 1905, the same year he published his first paper on special relativity. His explanation of the photoelectric effect was the basis for the Nobel Prize awarded to him in 1921. Although his other contributions to theoretical physics were also noted in that award, special and general relativity were not fully recognized in spite of having been partially verified by experiment by 1921. Although hero-worshipped, this great man never received Nobel recognition for his most famous work—relativity.

Calculating photon energy and the photoelectric effect: a violet light

(a) What is the energy in joules and electron volts of a photon of 420-nm violet light? (b) What is the maximum kinetic energy of electrons ejected from calcium by 420-nm violet light, given that the binding energy (or work function) of electrons for calcium metal is 2.71 eV?

Strategy

To solve part (a), note that the energy of a photon is given by E = hf size 12{E = ital "hf"} {} . For part (b), once the energy of the photon is calculated, it is a straightforward application of KE e = hf –BE size 12{"KE" rSub { size 8{e} } = ital "hf""–BE"} {} to find the ejected electron’s maximum kinetic energy, since BE is given.

Solution for (a)

Photon energy is given by

E = hf size 12{E = ital "hf"} {}

Since we are given the wavelength rather than the frequency, we solve the familiar relationship c = size 12{c=fλ} {} for the frequency, yielding

f = c λ . size 12{f= { {c} over {λ} } } {}

Combining these two equations gives the useful relationship

E = hc λ . size 12{E = { { ital "hc"} over {λ} } } {}

Now substituting known values yields

E = 6 . 63 × 10 –34 J s 3.00 × 10 8 m/s 420 × 10 –9 m = 4.74 × 10 –19 J . size 12{E = { { left (6 "." "63" times " 10" rSup { size 8{"–34"} } " J " cdot " s " right )` left (3 "." "00" times " 10" rSup { size 8{8} } " m/s" right )} over {"420 " times " 10" rSup { size 8{"–9"} } " m"} } =" 4" "." "74 " times " 10" rSup { size 8{"–19"} } " J"} {}

Converting to eV, the energy of the photon is

E = 4 . 74 × 10 –19 J 1 eV 1.6 × 10 –19 J = 2.96 eV . size 12{E = left (4 "." "74 " times " 10" rSup { size 8{"–19"} } " J " right ) { {1`"eV"} over {1 "." "6 " times " 10" rSup { size 8{"–19"} } `J} } =" 2" "." "96"`"eV"} {}

Solution for (b)

Finding the kinetic energy of the ejected electron is now a simple application of the equation KE e = hf –BE size 12{"KE" rSub { size 8{e} } = ital "hf""–BE"} {} . Substituting the photon energy and binding energy yields

KE e = hf – BE = 2 . 96 eV – 2 . 71 eV = 0 . 246 eV . size 12{"KE" rSub { size 8{e} } = ital "hf"" – BE "=" 2" "." "96 eV – 2" "." "71 eV "=" 0" "." "246 eV"} {}

Discussion

The energy of this 420-nm photon of violet light is a tiny fraction of a joule, and so it is no wonder that a single photon would be difficult for us to sense directly—humans are more attuned to energies on the order of joules. But looking at the energy in electron volts, we can see that this photon has enough energy to affect atoms and molecules. A DNA molecule can be broken with about 1 eV of energy, for example, and typical atomic and molecular energies are on the order of eV, so that the UV photon in this example could have biological effects. The ejected electron (called a photoelectron ) has a rather low energy, and it would not travel far, except in a vacuum. The electron would be stopped by a retarding potential of but 0.26 eV. In fact, if the photon wavelength were longer and its energy less than 2.71 eV, then the formula would give a negative kinetic energy, an impossibility. This simply means that the 420-nm photons with their 2.96-eV energy are not much above the frequency threshold. You can show for yourself that the threshold wavelength is 459 nm (blue light). This means that if calcium metal is used in a light meter, the meter will be insensitive to wavelengths longer than those of blue light. Such a light meter would be completely insensitive to red light, for example.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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Source:  OpenStax, College physics -- hlca 1104. OpenStax CNX. May 18, 2013 Download for free at http://legacy.cnx.org/content/col11525/1.1
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