Introduction to Quantum Theory

Question 1

Experimental observations that cannot be explained by classical physics but can be explained by quantum theory

Answer 1

Black - body radiation
The formation of emission and absorption spectra
the photoelectric effect

Question 2

E = nhf

Answer 2

E = Energy (J)
n = 0,1,2,3 etc...
f = frequency (Hz)
h = planck's constant ( 6.63x10^-34 Js)

Question 3

UV catastrophe

Answer 3

when short wavelenghts graph tend to infinity

Question 4

The bohr model of the atom

Answer 4

that electrons can orbit in these permitted stable orbits without emitting radiation and that the angular momentum of the electrons in these orbits is quantised..

Question 5

Angular momentum

angular momentum = mvr = nh/2π

Answer 5

m = mass of electron (kg)
v = linear velocity (ms-1)
r = radius of orbit (m)
h = planck's constant
n = an integer 1,2,3 etc...

Question 6

particle-like behaviour of waves

Answer 6

Young’s Double Slit Experiment

when electrons pass through a tiny opening or slit they produce diffraction fringes.

Question 7

wave-like behaviour of particles

Answer 7

Compton’s experiment

the scattering of x-rays from electrons is observed. The scattered photons have lower energy and therefore a longer wavelength due to a loss of momentum.

Question 8

de Broglie wavelength

λ = h/p

Answer 8

λ = de Broglie wavelength (m)
h = planck's constant
p = momentum of electron (kg m s-1)

Question 9

It is not possible to know the precise position

Answer 9

and the momentum of a quantum particle at the same instant

Question 10

It is not possible to know the precise lifetime

Answer 10

of a particle and the associated energy change at the same instant

Question 11

Δx Δpₓ ≥ h/4π

Answer 11

Δx = uncertainty in position (m)
Δpₓ = uncertainty in momentum (kg ms-1)
h = planck's constant
π = pi

Question 12

ΔE Δt ≥ h/4π

Answer 12

ΔE = uncertainty in energy (J)
Δt = uncertainty in time (s)
h = planck's constant
π = pi

Question 13

Implications of the Heisenberg uncertainty

Answer 13

Concept of quantum tunnelling
in which a quantum particle can exist in a position that according to classical physics, it has insufficient energy to occupy.

Question 14

how would you know if something couldn’t be regarded as a particle due to their de Broglie wavelength

Answer 14

λ is too small for interference to be observed thus it cannot be regarded as a particle

Question 15

It is not possible to measure accurately the position of an electron using visible light. Describe the effect of using a beam of X-rays rather than visible light on the measurement of the electron’s position and momentum.

Answer 15

λ is reduced for x - rays
Δx is reduced for x - rays
since Δx Δpₓ ≥ h/4π
Δpₓ increases

Question 16

how can particles escape a nucleus with energy much higher than it already has?

Answer 16

since ΔE Δt ≥ h/4π

Borrowing energy for a short period of time
allows particles to escape

Question 17

the expected graph of black body radiation with classical physics

Answer 17

check jotter
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Question 18

Black Body radiation

Answer 18

peak wavelength of this distribution is shorter for hotter objects than for cooler objects.