A preliminary study of blackbody radiation

Planck's blackbody radiation theory

Blackbody radiation

• In black ： An object that can completely absorb incoming electromagnetic waves of various wavelengths without reflecting .
• Blackbody radiation ： Black bodies do not reflect electromagnetic waves , But it can radiate electromagnetic waves , Such radiation is called blackbody radiation .
• Blackbody radiation is an ideal thermal radiation , Only related to temperature .
• Anything , As long as its temperature is above absolute zero , Just radiate around , This is called temperature radiation . As long as its temperature is above absolute zero , Also absorb radiant energy from the outside .
• The following figure shows the experimental results
  
• notes ： there $\nu$ Is the radiation frequency of the object , Similar to classical mechanics $f$.

The difficulties of classical theory

Riley - Kings formula

• According to classical electrodynamics and statistical mechanics, the formula of heat balance radiation energy distribution is derived .
• The formula is as follows ：$$w(v,T)=\frac{8\pi v^2}{c^3}kT$$
• $k$ It's Boltzmann constant ,$с$ Is the speed of light in vacuum ,$T$ Is the thermodynamic temperature .
• Riley - In the case of long wave or high temperature , It is consistent with the experimental results , But in the short wave range , The energy density increases rapidly and monotonically , Contradict the experimental results （ UV disaster ）.

Wayne's formula

• Based on thermodynamics and hypothesis, the formula of heat balance radiation energy distribution is derived .
• The formula is as follows ：$$w(v,T)=\frac{8\pi h{v}^3}{c^3}{e}^{-hv/kT}$$
• The Wien formula agrees with the experimental results in short wave , But in the long wave, the difference is large .
• Common characteristics of classical physics , Physical quantities are continuous , But they can't explain the blackbody radiation spectrum .
  
• Pay attention to distinguish between , The abscissa in the above figure is the wavelength , And in the first picture , The abscissa is the frequency , It's the reciprocal relationship , You can't confuse .

Planck's quantization of energy

• Mentioned earlier ： Common characteristics of classical physics , Physical quantities are continuous , But they can't explain the blackbody radiation spectrum .
• Energon ：
  • 1900 year , Planck proposed to explain the blackbody radiation spectrum , Energy can only be an integral multiple of a certain minimum energy .
  • The energy of the energetic particle is ：$\epsilon =hv$
  • among $h=6.626\ast 10^{-34}J\ast s$, It is called Planck constant .
• By quantizing , It is possible to derive a formula which is consistent with the experimental results of blackbody radiation . Refer to the above figure .
• Personal understanding of the Energon ：
  • Like a dollar coin , Now suppose that the smallest unit of money is 1 Yuan coins （ Not much ）, So now you need to buy something 100 block , Then I can only take out 100 A dollar coin to pay for this fee .
  • The smallest monetary unit mentioned earlier is 1 element , So the problem is , If the fee I have to pay is 99.5 Well ？ How did I close this deal through portfolio approach ？
  • In fact, in currency exchange , This situation itself will not occur , In other words, there will be no cost 99.5 The exchange of . in other words , In quantum , The energy exchange can only be an integral multiple of the smallest unit .