Quantum Mechanics and Probability; #1 Blackbody Radiation.

<Picture 1 ; Max Planck>

 

   In the last series, we talked about the Relativity and Twin Paradox. The relativity was a ground breaking theory at that time. In addition, the twin paradox is one of the most shocking conclusions in the relativity.

 

   For the following series of posts, I'm gonna tell you about the Quantum mechanics and its interpretation. It is the topic which made me interested in the physics.

 

 

1. Blackbody Radiation in the Classical Physics

 

<Picture 2 ; The Black Body>

 

   If someone turn the light on to his hand, some of the light's energy will be absorbed in the hand and the others will be emitted to outside. The rate of the absorbtion and emission is up to its materials.

  

   Then what is the blackbody? The blackbody is an ideal body which absorbs every energy but emits nothing. In the picture 2, the hole as an entrance is very very small so that the light can't come back to outside.

 

<Picture 3; Rayleigh and Jeans>

 

   Lord Rayleigh and James Jeans studied the blackbody radiation. They calculated the formula of blackbody radiation according to the classical physics. First, they found the equation for the density(G) of standing waves in blackbody.

 

The classical average energy per standing wave is as follows.

  

 

By multiplying it, they calculated the total energy density.

 

This is the Rayleigh-Jeans formula.

2. Inconsistency with the Experimental Data

 

   Rayleigh-Jeans formula contains everything that classical physics can say about the spectrum of blackbody radiation. But it was not identical to its experimental data.

 

<Picture 4 ; Inconsistency between the equation and experiment data>

 

   In picture 4, the led line is a graph of the Rayleigh-Jeans formula and the black line is a graph of the experimental data. In experiment, when the frequency is high, the energy converges to zero. But, according to the Rayleigh-Jeans formula, the energy is proportional to its frequency. So, this inconsistency was the limit of the classical physics.

 

3. Planck's Lucky Guess

  

   In 1900, the German physicist Max Planck used "lucky guesswork"(as he later called it) to come up with a formula for the blackbody radiation.

 

  In the equation, h is Planck's constant. It is just a constant. Don't care about it.

  According to this equation, when the frequency is high, the energy density converges to zero. In addition, when the frequency is low, this formula become identical to the Rayleigh-Jeans formula. (If you want to know the mathematical proof click HERE.)

   So, he just fixed the Rayleigh-Jeans formula with his lucky guess. But it was not just simple lucky guess. It was the jackpot in the physics. His work just opened the door of the quantum mechanics. Although he didn't expect that his work would change the paradigm of the physics, it was the beginning of the quantum mechanics.

   In the next post, we're gonna talk about the Schrodinger's Cat. The cat is famous because she is both alive and dead simultaneously. Isn't it weird to say that she is both alive and dead? See you in the next post. Thank you for reading it.

 

Bibiology

Arther Baiser, 2003, Concepts of Modern Physics(6th ed.), Boston : Mcgraw-Hill.

 

 

2016.04.29. Hankwanghee