Question

Find the meaning of the following base concepts ideas of Quantum mechanics:

The ultraviolet catastrophe
Schrödinger's cat
The wave particle duality

Answer 1

The ultraviolet catastrophe:

It is in short we can say as the error at short wavelengths in the Rayleigh–Jeans law.

An ideal body which emits and absorbs all frequencies is called black body.

The intensity of the emitted radiation depends upon the temperature of the black body as well as on the wavelength of the radiations emitted. The energy density of black body depends upon the temperature upto which it is heated. The distribution of this radiant energy over different frequencies is described in terms of energy density vs wavelength. These curves are known as black body radiation curves. Each curve follows following features:

For each temperature there is particular wavelength at which the energy radiated is maximum and the position of this maximum shifts towards lower wavelength with increase in temperature. Classical physics theory can be applied to derive an equation which describes the intensity of black body radiation as a function of frequency for a fixed temperature which is also known as the Rayleigh-Jeans law. This Rayleigh-Jeans law works for higher wavelengths λ, it diverges as wavelength λ become low in magnitude. This divergence for high frequencies is called the ultraviolet catastrophe.

Schrödinger's cat:

It is a famous hypothetical experiment carried out to define a flaw in the Copenhagen interpretation which states that atoms or photons exist in multiple states(all states) at once until they are being observed.

The virtual image of the experiment was that a cat is placed in a sealed box, with other objects such as (a bottle of poison, a radioactive sample, and a Geiger counter). If the Geiger counter detects that the radioactive material has decayed, it will trigger which will smash the bottle of poison and the cat can be assumed to be killed.

Schrödinger then claimed that quantum superposition can not be made to work with larger objects such as cats, because it is impossible for an organism to be alive and dead at the same time.

The wave particle duality:

The phenomena like black body radiations and photoelectric effect prove that electromagnetic waves have particle nature. de-Broglie presumed that material particles could also possess the wave nature i.e. matter cam have both particle as well as wave character.

The wave associated with this matter is called de-Broglie wave or matter wave.

According to Planck's quantum theory the energy of a photon is given by:

E = hv = hc/λ -------- (i)

and according to einstein, E = mc² --------(2)

comparing the values:

mc² = hc/λ

mc = h/λ

λ = h/mc -------------(3)

when above equation is applied to a material particle, the mass of photon is replaced by mass of particle and the velocity of light 'c' is replaced by velocity of particle 'v'.

Thus equation (3) becomes equal to

  λ = h/mv ------(4)

equation 4 shows that matter has dual nature of wave and particle.