Question

1. Explain the physical reason that this change in Planck's expression avoided the ‘Ultraviolet Catastrophe’.

2. Calculate the probability of finding the particle within the finite wall of the box when the particle is in the lowest and highest bound energy states of the box with one finite wall described above. Assume that the coefficient D is approximately D= (2/L)^1/2

Answer 1

1.

The ultraviolet catastrophe was the prediction of late 19^th century classical physics that an ideal blackbody at thermal equilibrium will emit radiation in all frequency ranges , emitting more energy as the frequency increases. The ultraviolet catastrophe results from the equipartition theorem of classical mechanics which states that all harmonic oscillator modes ( degrees of freedom) of a system at equilibrium have an average energy of (1/2)KT.

Planck derived the correct form for the intensity spectral distribution function by making sum strang assumptions.

Planck assumed that electromagnetic radiation can only be emitted or absorbed in descrete packets called quanta of energy.

E_quanta = h = h (c/ )

Where h is the planck's constant.

Planck's assumption led to the correct form of spectral distribution functiom :

B(,T) = (2hc²/⁵)×[1÷(e^hc/kT - 1)]

Albert Einstein solved the problem by postulating that planck's were real physical particles( called photons)

Photoelectric effect is the physical example.