Atomic george notes Flashcards
what is orbital angular momentum number displayed as
the letter l where:
l = 0 , 1, 2 , 3
how are the orbital angular momentum states labelled
using the letters s,p,d,f (0,1,2,3) for electrons and S,P,D,F (0,1,2,3) for atoms
rules from the schrodinger equation for the hydrogen atom
l =0,1,… , n-1
me=0,+-1, …. +-1 -> 2l+l me for a given l
what do quantum numbers l and me represent
they represent the measurables of orbital angular momentum
what is the magnitude of the angular momentum
root (l(l+1)) hbar
what is the projection of the orbital angular momentum onto the z axis
Lz = mihbar
how is a quantisation axis defined
by imposing a B field (put it in a magnet)
only one electron is involved in …. in a hydrogen atom or alkali metal
optical transitions
how is the spin of the electron in a hydrogen atom described
the spin angular momentum is described by the Q numbers Sand Ms
spin magnetic moment equation
mu_s =-g_s mu_B 1/hbar s , g_s =2
total ngular momentum equation
J=L+S
J=L+- 1/2
mu _J = -J , -J +1 , ….+ J -> 2J+1 values of mu_J
what does a continuous spectrum result from
A hot body where a wide varity of wavelengths are present
steps of a continuous spectrum spectroscopy
- 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
what do line spectrum result from
a gaseous light source, only certain frequencies of light are present. atoms with more electrons have more spectral lines.
band spectrum results from
band spectrum results from molecules: large numbers of lives that are lose together are observed.
what does spectroscopy measure
frequency but this means that the wavelength and energy can be determined from the spectroscopy through the frequency
both c= equations
c=v lambda = omega/k
k = equation
k=2pi/lambda
omega = equation
omega =2 pi /T
P (momentum) = equation
p=h/lambda = hbar K = h v /c = hbar omega / c
what did Einstein propose
the quantisation of ligh , which supported the discrete energy levels bohr postulate earlier.
absorption
a photon is removed from the energy field.
Delta E = E_1 - E_2 hv
spontaneous emission
photons can be radiated through spontaneous emission.
Delta E = hv
connection between momentum and photons
photons have momentum so atoms that absorb photons gain momentum and lose momentum when emitting a photon
The Balmer series equation
1/lambda = R (1/2^2 -1/n^2)
where n is an integer grater then2
R is a constant
hydrogen spectrum energy equation
E=hc/lambda = hcR(1/2^2 - 1/n^2) = 13.6 (1/2^2-1/n^2)eV
The rhydberg equation
1/lambda=R (1/n2^2 - 1/n1^2)
n2
what led to the discovery of the rhydberg equation
looking at the balmer series and other spectral lines suggested it
bohrs first postulate
electrons move in circular orbits around the nucleus classically obeying the coulomb attraction.
what did the bohrs first postulate show
the existence of the nucleus
bohrs second postulate
the permitted orbit have quantised angular momentum L=nhbar
what did bohrs second postulate show
introduction of quantisation
bohrs third postulate
the electrons are stable in their orbits with constant energy ]
bohrs 4th postulate
absoption and emission occur from the movement of an electron between two stable orbits
E = hf = hbar ω
central force in the bohr orbit is
F = -ke^2 z/r^2 = -mv^2/r
angular momentum is quantised equation
L=nhbar
n is the principle quantum number,
hbar s the base unit of angular momentum
what additional information does the eigenfunction of the schrodinger equation contain
probability density
electron spin
transition rates
