# 29.2 The photoelectric effect  (Page 3/8)

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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 $E=\text{hf}$ . For part (b), once the energy of the photon is calculated, it is a straightforward application of ${\text{KE}}_{e}=\text{hf}\text{–BE}$ to find the ejected electron’s maximum kinetic energy, since BE is given.

Solution for (a)

Photon energy is given by

$E=\text{hf}$

Since we are given the wavelength rather than the frequency, we solve the familiar relationship $c=\mathrm{f\lambda }$ for the frequency, yielding

$f=\frac{c}{\lambda }.$

Combining these two equations gives the useful relationship

$E=\frac{\text{hc}}{\lambda }.$

Now substituting known values yields

$E=\frac{\left(6\text{.}\text{63}×{\text{10}}^{\text{–34}}\phantom{\rule{0.25em}{0ex}}\text{J}\cdot \text{s}\right)\left(3.00×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s}\right)}{\text{420}×{\text{10}}^{\text{–9}}\phantom{\rule{0.25em}{0ex}}\text{m}}=\text{4.74}×{\text{10}}^{\text{–19}}\phantom{\rule{0.25em}{0ex}}\text{J}.$

Converting to eV, the energy of the photon is

$E=\left(4\text{.}\text{74}×{\text{10}}^{\text{–19}}\phantom{\rule{0.25em}{0ex}}\text{J}\right)\frac{1 eV}{1.6×{\text{10}}^{\text{–19}}\phantom{\rule{0.25em}{0ex}}J}=\text{2.96 eV}.$

Solution for (b)

Finding the kinetic energy of the ejected electron is now a simple application of the equation ${\text{KE}}_{e}=\text{hf}\text{–BE}$ . Substituting the photon energy and binding energy yields

${\text{KE}}_{e}=\text{hf}\text{– BE}=\text{2}\text{.}\text{96 eV – 2}\text{.}\text{71 eV}=\text{0}\text{.}\text{246 eV}.$

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

What does mean ohms law imply
what is matter
Anything that occupies space
Kevin
Any thing that has weight and occupies space
Victoria
Anything which we can feel by any of our 5 sense organs
Suraj
Right
Roben
thanks
Suraj
what is a sulphate
Alo
Alo
the time rate of increase in velocity is called
acceleration
Emma
What is uniform velocity
Victoria
Greetings,users of that wonderful app.
how to solve pressure?
how do we calculate weight and eara eg an elefant that weight 2000kg has four fits or legs search of surface eara is 0.1m2(1metre square) incontact with the ground=10m2(g =10m2)
Cruz
P=F/A
Mira
can someone derive the formula a little bit deeper?
Bern
what is coplanar force?
what is accuracy and precision
How does a current follow?
follow?
akif
which one dc or ac current.
akif
how does a current following?
Vineeta
?
akif
AC current
Vineeta
AC current follows due to changing electric field and magnetic field.
akif
you guys are just saying follow is flow not follow please
Abubakar
ok bro thanks
akif
flows
Abubakar
but i wanted to understand him/her in his own language
akif
but I think the statement is written in English not any other language
Abubakar
my mean that in which form he/she written this,will understand better in this form, i write.
akif
ok
Abubakar
ok thanks bro. my mistake
Vineeta
u are welcome
Abubakar
what is a semiconductor
substances having lower forbidden gap between valence band and conduction band
akif
what is a conductor?
Vineeta
replace lower by higher only
akif
convert 56°c to kelvin
Abubakar
How does a current follow?
Vineeta
A semiconductor is any material whose conduction lies between that of a conductor and an insulator.
AKOWUAH
what is Atom? what is molecules? what is ions?
What is a molecule
Is a unit of a compound that has two or more atoms either of the same or different atoms
Justice
A molecule is the smallest indivisible unit of a compound, Just like the atom is the smallest indivisible unit of an element.
Rachel
what is a molecule?
Vineeta
what is a vector
A quantity that has both a magnitude AND a direction. E.g velocity, acceleration, force are all vector quantities. Hope this helps :)
deage
what is the difference between velocity and relative velocity?
Mackson
Velocity is the rate of change of displacement with time. Relative velocity on the other hand is the velocity observed by an observer with respect to a reference point.
Chuks
what do u understand by Ultraviolet catastrophe?
Rufai
A certain freely falling object, released from rest, requires 1.5seconds to travel the last 30metres before it hits the ground. (a) Find the velocity of the object when it is 30metres above the ground.
Mackson
A vector is a quantity that has both magnitude and direction
Rufus
the velocity Is 20m/s-2
Rufus
derivation of electric potential
V = Er = (kq/r^2)×r V = kq/r Where V: electric potential.
Chuks
what is the difference between simple motion and simple harmonic motion ?
syed
hi
Peace
hi
Rufus
hi
Chip
simple harmonic motion is a motion of tro and fro of simple pendulum and the likes while simple motion is a linear motion on a straight line.
Muinat
a body acceleration uniform from rest a 6m/s -2 for 8sec and decelerate uniformly to rest in the next 5sec,the magnitude of the deceleration is ?
The wording not very clear kindly
Moses
6
Leo
9.6m/s2
Jolly
the magnitude of deceleration =-9.8ms-2. first find the final velocity using the known acceleration and time. next use the calculated velocity to find the size of deceleration.
Mackson
wrong
Peace
-3.4m/s-2
Justice
Hi
Abj
Firstly, calculate final velocity of the body and then the deceleration. The final ans is,-9.6ms-2
Muinat
8x6= 48m/-2 use v=u + at 48÷5=9.6
Lawrence
can i define motion like this motion can be define as the continuous change of an object or position
Any object in motion will come to rest after a time duration. Different objects may cover equal distance in different time duration. Therefore, motion is defined as a change in position depending on time.
Chuks