Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium based on two parameters: temperature and frequency or wavelength. It provides a distribution that peaks at a certain wavelength, with the peak shifting to shorter wavelengths at higher temperatures. Planck proposed that the light energy emitted by a black body is quantized in units of Planck's constant h multiplied by the frequency of light. This resolved the ultraviolet catastrophe and established the foundation for quantum mechanics.

1. Plancks Law

2. Planck Law
- We have two forms. As a function of wavelength.
1
1
5
2
2
)
,
(


kT
hc
e
hc
T
I



2
Planck’s Law
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3. Planck Law
And as a function of frequency
3
1
1
2
)
,
( 2
3


kT
h
e
c
h
T
I



Planck’s Law
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4. The Planck Law gives a distribution that peaks
at a certain wavelength.
4
Planck’s Law
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5. The peak shifts to shorter wavelengths for
higher temperatures
5
Planck’s Law
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6. The area under the curve grows rapidly with
increasing temperature.
6
Planck’s Law
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7. • Planck (1900) proposed that the light energy
emitted by the black body is quantized in units of
h ( = frequency of light).
Planck’s Law
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8. Planck (1900) proposed that the light energy emitted
by the black body is quantized in units of h ( =
frequency of light).
E = nh (n = 1, 2, 3, …)
Planck’s Law
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9. Planck (1900) proposed that the light energy emitted
by the black body is quantized in units of h ( =
frequency of light).
E = nh (n = 1, 2, 3, …)
High frequency light only emitted if thermal energy
kT  h.
Planck’s Law
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10. Planck (1900) proposed that the light energy emitted
by the black body is quantized in units of h ( =
frequency of light).
E = nh (n = 1, 2, 3, …)
High frequency light only emitted if thermal energy
kT  h.
h – a quantum of energy.
Planck’s Law
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11. Planck (1900) proposed that the light energy emitted by
the black body is quantized in units of h ( = frequency
of light).
E = nh (n = 1, 2, 3, …)
High frequency light only emitted if thermal energy kT 
h.
h – a quantum of energy.
Planck’s constant h ~ 6.6261034 Js
Planck’s Law
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12. Planck (1900) proposed that the light energy emitted by
the black body is quantized in units of h ( = frequency
of light).
E = nh (n = 1, 2, 3, …)
High frequency light only emitted if thermal energy kT 
h.
h – a quantum of energy.
Planck’s constant h ~ 6.6261034 Js
If h  0 we regain classical mechanics.
Planck’s Law
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13. Planck (1900) proposed that the light energy emitted by the
black body is quantized in units of h ( = frequency of light).
E = nh (n = 1, 2, 3, …)
High frequency light only emitted if thermal energy kT  h.
h – a quantum of energy.
Planck’s constant h ~ 6.6261034 Js
If h  0 we regain classical mechanics.
Conclusions:
• Energy is quantized (not continuous).
• Energy can only change by well defined amounts.
Planck’s Law
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14. 14
Comparison of Rayleigh-Jeans law with Wien's law and Planck's law,
for a body of 8 mK temperature.
Planck’s Law
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