Quantum effects - Structure of matter Flashcards
Are the laws of classical physics sufficinet to describe the physcial processes in the world of atoms?
NO.
Within regions of very small distances, we can meet other processes, which are not known in out macro-world and new physcial quantities.
What is ‘the effect’?
‘The effect’ is related to the
- Planck’s constant, h
or
- Dirac’s constant, ħ = 1.05 * 10-34J.s.
These constants are related by the equation
ħ = h/(2π)
Explain angular momentum and furthermore the vector product.
One of the effects of quantum properties is discrete value of the angular momentum.
The angular momentum, L, is defined as a vector product (cross product) of the postion vector, r, and of the vector momentum p=mv.
L = [r * p]
In general the vector product of two vectors is a vector perpendicular to the plane determined byt he vectors multiplied and its magnitude equals the product of their magnitudes multiplied by the sine of their angle.
As seen in the figure, considering the regular circular motion, directions of momentum vector v and of position vector r change at every moment while their vector product remains constant with respect to its magnitude and direction.
The vectors r and v are perpendicular to each other, and thus the magnitude of angular momentum L = rmc, since sin(π/2) = 1.
Describe angular momentum of elementary particles
Besides the orbital angular momentum, elementary particles also possess their own angular momentum, spin, and magnetic moment due to rotation.
The particles with half-value spin are called Fermi particles (ferions) while those with integer values of spin are called Bose particles (bosons).
E.g. The spin of electron or of nucleon equals 1/2, the spin of photon equals 1 (in multiples of ħ).
The value of spin determines the behaviour of particle.
Thus, Fermi particles with identical spin cannot exist at the same energy level.
This explains why all the electrons in heavy atoms do not occupy the lowest energy level but also higher energy levels, more distanced from the nucleus.
On the other hand, Bose particles tend to occupy the same energy state.
Explain the properties possessed by elementary particles and how these properties were demonstrated.
Elementary particles as well as their system (atom, molecule) possess both corpuscular and wave properties.
This fact was originally estimated from the properties of light.
Interference or diffraction of light proves that light is represented by waves, while photoelectric effect demonstrates that light is a flux of quanta of energy, photons.
The energy, E, of a photon (J) is related to the frequency f(s-1) of the wave and to its wavelength, λ, (m) by equation:
E = hf = (hc)/λ
- c = velocity of light in vacuum
- h = 6.63*10-34
- J.s = 4.13*10-15eV.s is the Planck’s constant.
The motion of each particle with the
- Mass (m)
- Momentum (p)
- Energy (E)
is related to the wavelengths λ of the deBroglie’s wave equation.
λ = h/p = h/√(2mE)
and to the frequency f by equation
f = E/h
The equation λ = h/p = h/√(2mE) reveals that the wavelengths of elementary particals are very short.
Describe the corpuscular wave dualism of subatomic particles.
The corpuscular-wave dualism of subatomic particles has its consequences.
It is not possible to estimate simultaneously the position vector, r, of the particle (or its coordinates) and its momentum, p, with an arbitrary accuracy.
The Heisenberg’s relation of uncertainty holds for the uncertainty of the position vector, Δr and of the momentus Δp.
Δr.Δp ≥ ћ
Therefore if the given energy state lasts for a long time, its energy may be estabished with a high degree of certainty.
Quantum effects are quantitatively described by quantum mechanics.
