Atomic george notes

Question 1

what is orbital angular momentum number displayed as

Answer 1

the letter l where:

l = 0 , 1, 2 , 3

Question 2

how are the orbital angular momentum states labelled

Answer 2

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

Question 3

rules from the schrodinger equation for the hydrogen atom

Answer 3

l =0,1,… , n-1

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

Question 4

what do quantum numbers l and me represent

Answer 4

they represent the measurables of orbital angular momentum

Question 5

what is the magnitude of the angular momentum

Answer 5

root (l(l+1)) hbar

Question 6

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

Answer 6

Lz = mihbar

Question 7

how is a quantisation axis defined

Answer 7

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

Question 8

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

Answer 8

optical transitions

Question 9

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

Answer 9

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

Question 10

spin magnetic moment equation

Answer 10

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

Question 11

total ngular momentum equation

Answer 11

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

Question 12

what does a continuous spectrum result from

Answer 12

A hot body where a wide varity of wavelengths are present

Question 13

steps of a continuous spectrum spectroscopy

Answer 13

• 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

Question 14

what do line spectrum result from

Answer 14

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

Question 15

band spectrum results from

Answer 15

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

Question 16

what does spectroscopy measure

Answer 16

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

Question 17

both c= equations

Answer 17

c=v lambda = omega/k

Question 18

k = equation

Answer 18

k=2pi/lambda

Question 19

omega = equation

Answer 19

omega =2 pi /T

Question 20

P (momentum) = equation

Answer 20

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

Question 21

what did Einstein propose

Answer 21

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

Question 22

absorption

Answer 22

a photon is removed from the energy field.

Delta E = E_1 - E_2 hv

Question 23

spontaneous emission

Answer 23

photons can be radiated through spontaneous emission.

Delta E = hv

Question 24

connection between momentum and photons

Answer 24

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

Question 25

The Balmer series equation

Answer 25

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

where n is an integer grater then2

R is a constant

Question 26

hydrogen spectrum energy equation

Answer 26

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

Question 27

The rhydberg equation

Answer 27

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

n2

Question 28

what led to the discovery of the rhydberg equation

Answer 28

looking at the balmer series and other spectral lines suggested it

Question 29

bohrs first postulate

Answer 29

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

Question 30

what did the bohrs first postulate show

Answer 30

the existence of the nucleus

Question 31

bohrs second postulate

Answer 31

the permitted orbit have quantised angular momentum L=nhbar

Question 32

what did bohrs second postulate show

Answer 32

introduction of quantisation

Question 33

bohrs third postulate

Answer 33

the electrons are stable in their orbits with constant energy ]

Question 34

bohrs 4th postulate

Answer 34

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

Question 35

central force in the bohr orbit is

Answer 35

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

Question 36

angular momentum is quantised equation

Answer 36

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

Question 37

what additional information does the eigenfunction of the schrodinger equation contain

Answer 37

probability density
electron spin
transition rates