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1
Q

what is orbital angular momentum number displayed as

A

the letter l where:

l = 0 , 1, 2 , 3

2
Q

how are the orbital angular momentum states labelled

A

using the letters s,p,d,f (0,1,2,3) for electrons and S,P,D,F (0,1,2,3) for atoms

3
Q

rules from the schrodinger equation for the hydrogen atom

A

l =0,1,… , n-1

me=0,+-1, …. +-1 -> 2l+l me for a given l

4
Q

what do quantum numbers l and me represent

A

they represent the measurables of orbital angular momentum

5
Q

what is the magnitude of the angular momentum

A

root (l(l+1)) hbar

6
Q

what is the projection of the orbital angular momentum onto the z axis

A

Lz = mihbar

7
Q

how is a quantisation axis defined

A

by imposing a B field (put it in a magnet)

8
Q

only one electron is involved in …. in a hydrogen atom or alkali metal

A

optical transitions

9
Q

how is the spin of the electron in a hydrogen atom described

A

the spin angular momentum is described by the Q numbers Sand Ms

10
Q

spin magnetic moment equation

A

mu_s =-g_s mu_B 1/hbar s , g_s =2

11
Q

total ngular momentum equation

A

J=L+S
J=L+- 1/2
mu _J = -J , -J +1 , ….+ J -> 2J+1 values of mu_J

12
Q

what does a continuous spectrum result from

A

A hot body where a wide varity of wavelengths are present

13
Q

steps of a continuous spectrum spectroscopy

A
  • the source is shone through a slit
  • the beam is split by a diffraction grating or prism
  • the lens focusses the light
  • the spectrum is displayed on the screen
14
Q

what do line spectrum result from

A

a gaseous light source, only certain frequencies of light are present. atoms with more electrons have more spectral lines.

15
Q

band spectrum results from

A

band spectrum results from molecules: large numbers of lives that are lose together are observed.

16
Q

what does spectroscopy measure

A

frequency but this means that the wavelength and energy can be determined from the spectroscopy through the frequency

17
Q

both c= equations

A

c=v lambda = omega/k

18
Q

k = equation

A

k=2pi/lambda

19
Q

omega = equation

A

omega =2 pi /T

20
Q

P (momentum) = equation

A

p=h/lambda = hbar K = h v /c = hbar omega / c

21
Q

what did Einstein propose

A

the quantisation of ligh , which supported the discrete energy levels bohr postulate earlier.

22
Q

absorption

A

a photon is removed from the energy field.

Delta E = E_1 - E_2 hv

23
Q

spontaneous emission

A

photons can be radiated through spontaneous emission.

Delta E = hv

24
Q

connection between momentum and photons

A

photons have momentum so atoms that absorb photons gain momentum and lose momentum when emitting a photon

25
Q

The Balmer series equation

A

1/lambda = R (1/2^2 -1/n^2)

where n is an integer grater then2

R is a constant

26
Q

hydrogen spectrum energy equation

A

E=hc/lambda = hcR(1/2^2 - 1/n^2) = 13.6 (1/2^2-1/n^2)eV

27
Q

The rhydberg equation

A

1/lambda=R (1/n2^2 - 1/n1^2)

n2

28
Q

what led to the discovery of the rhydberg equation

A

looking at the balmer series and other spectral lines suggested it

29
Q

bohrs first postulate

A

electrons move in circular orbits around the nucleus classically obeying the coulomb attraction.

30
Q

what did the bohrs first postulate show

A

the existence of the nucleus

31
Q

bohrs second postulate

A

the permitted orbit have quantised angular momentum L=nhbar

32
Q

what did bohrs second postulate show

A

introduction of quantisation

33
Q

bohrs third postulate

A

the electrons are stable in their orbits with constant energy ]

34
Q

bohrs 4th postulate

A

absoption and emission occur from the movement of an electron between two stable orbits
E = hf = hbar ω

35
Q

central force in the bohr orbit is

A

F = -ke^2 z/r^2 = -mv^2/r

36
Q

angular momentum is quantised equation

A

L=nhbar
n is the principle quantum number,
hbar s the base unit of angular momentum

37
Q

what additional information does the eigenfunction of the schrodinger equation contain

A

probability density
electron spin
transition rates