The image above is a blackbody. Yes, for some perhaps who may not have heard of this perplexing area of physics might be confused. However, I can assure you the sun is one of the best examples of a blackbody we have. Another is cosmic background radiation, which as you will see fits a similar description.
So what is a blackbody?
A blackbody is an idealised object that absorbs all incident radiation on it and emits radiation of all wavelengths. The intensity emitted radiation of each wavelength is dependant on the temperature of the object.
Real objects never fully behave as blackbodies, as the wavelength emission is a often a fraction of what is would be ideally.
Emissivity
Emissivity describes how well a real object can radiate energy relative to a blackbody. Hence by definition a black body has an emissivity e = 1.0
In practice most objects considered to be blackbodies have an emissivity approaching 0.99. Sources with lower emissivities are often called grey bodies.
| Material | Emissivity |
| Asphalt pavement | 0.9 |
| Aluminium foil | 0.07 |
| Polished gold | 0.03 |
Absorptivity
Absorptivity aλ is the ratio of energy absorbed by an object E(a) to the energy incident on the object E(i) for a particular wavelength.
According to Kirchhoff when a blackbody is in thermal equilibrium the absorptivity is equal to the emissivity.
https://en.wikipedia.org/wiki/Kirchhoff%27s_law_of_thermal_radiation
The radiancy of a blackbody i.e the characteristic intensity-wavelength curve is identical for all other blackbodies at the same temperature at thermal equilibrium.
Wein’s Displacement Law
Wein’s displacement law took into consideration that all the peaks of the blackbody radiation curves can be a connected by a constant. Wein noted that the product of the maximum wavelength and the temperature always yielded the same constant. This constant was found to be 2.898 x 10-3 mK (meter Kelvin).
Max Planck was the first scientist to develop a mathematical function that accurately described the blackbody radiation curves and integrate the early formulations of quantum mechanics.
Planck showed that the intensity of the radiation given off from a blackbody is a function of the temperature and wavelength.
Where I is the intensity of the blackbody radiation, c is the speed of light, λ is the wavelength of light, h is planck’s constant and k is the Boltzman constant.
Planck helped developed the idea that energy is not emitted or absorbed continuously but is quantized and comes in discrete amounts. This is the basis on which quantum mechanics is built.
Some Python Code
#program by Clement Charles
import numpy as np
from matplotlib import pyplot as plt
T = float(input(("Enter temp. of blackbody: ")))
u = 0.1*(10**-9)
I = []
x = 0.0
wavelength = []
count = 100000
#this value must be increased for low temperatures to allow more permutations
inte = 0.0
c = 2 * 3.141 * 3*(10**6)*6.62607004*(10**-34)
h_ = 3*(10**6)*6.62607004*(10**-34)
k = 1.38064852*(10**-23)
def f(x):
return (c/(x**5))*(1/np.exp((h_/(x*k*T))))
for i in range(count):
x = x + u
wavelength.append(x)
inte = f(x)
I.append(inte)
temp = str(T)
title = 'Blackbody curve at a temp. of ', temp, "K"
plt.plot(wavelength, I)
plt.title(title)
plt.xlabel('wavelength (m)')
plt.ylabel('Intensity')
plt.grid(True)
plt.show()
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Quantum Mechanics Notes 