Blackbody Radiation

All normal matter at temperatures above absolute

zero emits electromagnetic radiation

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 An object that absorbs ALL radiation falling on it, at
all wavelengths, is called a blackbody.
When a blackbody is at a uniform temperature, its
emission has a characteristic frequency
distribution that depends on the temperature. This
emission is called blackbody radiation.

A room temperature blackbody appears

black, as most of the energy it radiates
is infra-red and cannot be perceived by
the human eye. When it becomes a
little hotter, it appears dull red. As its
temperature increases further it
becomes yellow, white, and ultimately
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blue-white.
The Sun, whose surface
temperature is in the range
between 5000 K and 6000 K,
radiates most strongly in a range of
wavelengths about 560 nm in the
visible part of the electromagnetic
spectrum.

Your body, when at its normal

temperature of about 300 K,
radiates most strongly in the
infrared part of the spectrum.
 Blackbody radiation graph
At relatively low temperatures,
most radiation is emitted at
wavelengths longer than 700
nm, which is in the infrared
portion of the spectrum. As the
temperature of the object
increases, the maximum
intensity shifts to shorter
wavelengths, successively
resulting in orange, yellow, and
finally white light.

At high temperatures, all Experimental relationship between the

wavelengths of visible light are temperature of an object and the spectrum
emitted. The white light of blackbody radiation it emits.
spectrum shown for an object
at 5000 K closely approximates
the spectrum of light emitted by 4
the sun.
 Ultraviolet catastrophe

A theory developed by Rayleigh and Jeans based on classical

theory predicted that the intensity should go to infinity at short
wavelengths. This is called ultraviolet catastrophe .

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Planck explain the spectral distribution of blackbody
radiation as result from oscillations of electrons.

He proposed that these oscillators not to radiate

energy (E) continuously, as the classical theory
would demand, but they could only lose or gain
energy in chunks, called quanta, of size hn, for an
oscillator of frequency n.

Planck constructed a new theory described by the

equation:
E= nhn
where n is any integer (1, 2, 3, …)
h is Planck’s constant (h =6.626×10−34 J⋅s)
n is frequency.
Planck’s theoretical result (continuous
curve) and the experimental blackbody
radiation curve (dots)

Conclusions:
Energy is quantized (not continuous).
Energy can only change by well defined amounts. 8
 The Photoelectric Effect
" When light shines on the surface of a metallic substance,
electrons in the metal absorb the energy of the light and they
can escape from the metal's surface. This is called the
photoelectric effect, and it is used to produce the electric
current ."

One of the most popular concepts concerning Quantum Mechanics is

called , “The Photoelectric Effect”. In 1905, Albert Einstein published this
theory for which he won the Nobel Prize in 1921.
The Photoelectric Effect
 The Photoelectric Effect
There are important aspects of the photoelectric
effect that could not explained by classical
mechanics:
 Threshold frequency:
Electrons are not emitted if light is below a certain
frequency. No matter how bright the light.

 No lag time :
Even at very low intensity, electrons are emitted

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• Below the threshold no electrons are ejected no
matter how long the light shines or how intense
(bright) it is.

Experiments show that if light of a certain

frequency can eject electrons from a metal, it 12

makes no difference how dim the light is.

 Photoelectric Effect (Einstein 1905)
Basics of Quantum Mechanics
hn Photoelectrons ejected with
- 
eo kinetic energy:
eP h telectrons
Ek = hn - F

Metal surface
work function = F

• No electrons are ejected (regardless of light intensity) unless

n exceeds a threshold value characteristic of the metal.

• Ek independent of light intensity but linearly dependent on n.

• Even if light intensity is low, electrons are ejected if n is above

the threshold.
 How do Photons Explain the Photoelectric Effect
• Low frequency (low energy) light does not eject
electrons from metal
 No matter how intense (bright)
 These photons don’t have enough energy and they don’t
sum or add up

• High frequency (high energy) light does eject

electrons
 Even if the light is dim
 These photons have enough energy – right frequency

Remember amplitude (or intensity/brightness) is not energy –

frequency/color is energy 14
Work function(binding energy), F , is defined as the
least energy that must be supplied to remove a free
electron from the surface of the metal, against the
attractive forces of surrounding positive ions.

An individual photon can give all of its energy to an

electron. The photon’s energy is partly used to break
the electron away from the material. The remainder
goes into the ejected electron’s kinetic energy. In
equation form, this is given by:

Ek = hn - F
 Ek = hn - F

where EK is the maximum kinetic energy of the ejected

electron, hn is the photon’s energy, and F binding
energy is the binding energy of the electron to the
particular material.

This equation explains the properties of the photoelectric

effect quantitatively and demonstrates that binding
energy is the minimum amount of energy necessary to
eject an electron. If the energy supplied is less than
binding energy, the electron cannot be ejected.
 Einstein’s Explanation
• Einstein proposed that the light energy was delivered to
the atoms in packets like a particle., called quanta or
photons.
• When the photon hits the metal, its energy, hν is taken
up by the electron.
• The energy of a photon of light is directly proportional
to its frequency.
 Inversely proportional to its wavelength
 The proportionality constant is called Planck’s Constant, (h),
and has the value 6.626 × 10−34 J ∙ s.
 Wave-Particle Duality
The results of the photoelectric effect allowed us
to look at light completely different.
First we have Thomas Young’s
Diffraction experiment proving
that light behaved as a WAVE
due to constructive and
destructive interference.

Then we have Max Planck who allowed Einstein to build his

photoelectric effect idea around the concept that light is composed of
PARTICLES called quanta.
Determine the increment of energy (the energy of a
photon of light) that is emitted by light with a
frequency of 1.42 x 1018 /s. The value of Planck’s
constant is 6.626 x 10 – 34 Js.

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Calculate the energy (in joules) of a photon
with a wavelength of 700.0 nm

109 m
  700.0 nm   7.00 107 m
nm
3.00 108 m/s
 7
 4.29  1014 1
s
7.00 10 m

E  (6.631034 J  s)(4.291014 s1 )

19
E  2.84 10 J
Calculate the wavelength (in nm) of light with energy
7.83 x 1019 J per photon. In what region of the
electromagnetic radiation does this light fall?

7.831019 J
 34
 1.18  1015 1
s
6.6310 J  s
1
3.00 10 m  s
8
 15 1
7
 2.5310 m or 253 nm
1.1810 s
Ultraviolet region
• Dual nature of light:
 Electromagnetic radiation (and all matter) exhibits
wave properties and particulate properties.

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 Compton effect
Further confirmation of the particle model of electromagnetic
radiation.
• Compton Effect was discovered by Arthur Holly Compton in
1923 and for this discovery he was awarded by the Nobel
Prize in Physics in 1927.

• According to classical theory of scattering, the wavelength

of X-ray would not be changing (Thomson scattering) after
interaction with the electrons, however Compton did find a
change in wavelength in experiment. Then Compton Effect
was explained on the basis of the quantum theory (particle
“photon” model) of light.

• This effect constitutes very strong evidence in support of

the Quantum Theory of radiation.
 The Compton Effect
In 1924, A. H. Compton performed an experiment where X-rays
impinged on matter, and he measured the scattered radiation.

λ𝑓 < λ𝑖
It was found that the scattered X-ray did not have the same
wavelength !
Compton explained his experimental results by
postulating that incident X-rays beam is assembly of
photons having energy E = hn . These photons make
collisions with free electrons in the scattering target .
The incident photon transfer some of its energy to
the free electron during collision so scattered photon
must have reduced energy. It means scattered
photon has large wavelength than incident photon .
This explains the wavelength shift in spectrum of
Compton effect.