5. ATOMIC MASS
1 atomic mass unit “amu”
= 1/12 of the mass of 12C atom
The carbon-12 atom has a mass of 12.000 u, and yet it contains
12 objects (6 protons and 6 neutrons) that each have a mass
greater than 1.000 u, not to mention a small contribution from the
6 electrons.
6. MASS DEFECT
Mass of nucleus < sum of p + n + e !
Why ?
Some of the mass is converted to be the BINDING
ENERGY of the nucleus that holds it together -> “mass
defect”
For 12C:
Mass defect = Dm = 6 * 1.008664 u + 6 * 1.007276 u +
6 * 0.00054858 u - 12.000 u = 0.098931 u
The binding energy in the carbon-12 atom is therefore
0.098931 u * 931.5 MeV/u = 92.15 MeV
(binding energies for electrons is just some eV !)
10. SOLUTION
Cl can have 18 or 20 neutrons
35.45 is a mix of 2/3 35Cl and 1/3 37Cl
Element number
= no. of protons
= no. of electrons
Mass number, not integer !
=> mix of ISOTOPES with
different no. of neutrons !
Z
A
11. ISOTOPES
Nearly all elements have isotopes,
that means the same elements
(no. of protons = Z) has different no. of
neutrons, and therefore different mass
Example:
Copper exists to 69.2% of 63Cu and the rest of
65Cu with masses 62.93 and 64.93
what is the atomic mass of the mixture ?
12. ISOTOPES AND MS
Isotope patterns are important to identify
fragments in MS
For example:
15. WHERE DO THE LINES COME FROM ?
Bohr (1913)
emission spectra of hydrogen gas
Lines correspond to energies that are
emitted by electrons:
emitted
16.
17. ELECTRONS ARE “FIXED” ON ORBITS !
Electrons can move between distinct
energy levels, they cannot exist just
anywhere in the atom = quantum
18. THE HYDROGEN EMISSION SPECTRUM
Electrical charged hydrogen gas will emit a
blue color and also UV radiation
21. How many lines in the emission spectrum
and at which energies (in cm-1) ?
22. Solution: 3 levels 3 lines
Transition A:
∆E = E3 – E2 =
-20’000 + 50’000 cm-1 =
30’000 cm-1 =
λ = 1/30’000cm-1 * 107 nm/1 cm = 333 nm
We can express energy as wavenumber,
because h and c are constant:
= const * 1/λ = const * ν
23. RYDBERG EQUATION
From which energy level does an electron
come to n=2 when visible light of 410 nm is
emitted ?
What is the Ionization energy of hydrogen
from this formula ?
-1
24. ELECTRONS AS WAVES
Electrons can be regarded to be waves
instead of particles.
DeBroglie:
26. ENERGY OF “WAVE-ELECTRONS”
We can model the behavior of an electron
in a restricted area
(“particle in a box”)
Quantization comes from
the fact that a wave has
to “fit” into the boundaries
27. Only wavelengths are allowed:
Use in DeBroglie:
Therefore the kinetic energy is:
n is the main quantum number
indicating the energy level
28. 3 QUANTUM NUMBERS
Because a particle is moving in 3D, we also
get 3 quantum numbers
n: main quantum number (start with 1)
l : angular “ ( 0,1 .. n-1)
m: magnetic “ ( -l … 0 … +l )
Electrons can live only in these “orbitals”
(spaces) defined by 3 quantum numbers
Up to 2 electrons can exist in one orbital
29. WATCH A DEMO VIDEO
http://www.youtube.com/watch?v=Fw6dI7cguCg
30. Main spectral lines = n
Fine structure = l
With magnetic field:
Zeeman effect
magnetic quantum no. m
31. QUESTIONS
How many orbitals are possible for the
energy level n = 2
and how many electrons can live there
maxium ?
n = 2
l = 0 and 1 (“s” and “p” level)
m = 0 and -1, 0, +1 (px, y and z)
36. ELECTRON SHIELDING
The nuclear charge experienced by an
electron is reduced by shielding by other
electrons.
Trends in effective nuclear charge can be
used to rationalize the trends in many
properties.
As a result of the combined effects of
penetration and shielding, the order of
energy levels in a shell of a many electron
atom is s < p < d < f
(Atkin p.16)
37. ELECTRON SHEILDING
Different from
Hydrogen, there are
electron-electron
interactions in the other
elements
Each electron experiences an effective
nuclear charge: Zeff = Z - σ
38. EXAMPLE LI (1S2 2S1)
The PAULI-EXCLUSION PRINCIPLE says
that no 2 electrons can have the same 4
quantum numbers (n l m and s)
=> the 1s orbital can not have 3 electrons, but
max. 2 (n=1, l=0, m=0, s= +/- ½)
=> The 3rd electron goes to the next energy
level n=2, but now, into s or p level ?
39. LI ELECTRON CONFIGURATION
Because of the form
of the function of 2s
it has electron density
closer to the nucleus
than 2p
less shielding by
1s electrons
lower energy
40. Z EFF FOR LI ELECTRONS
The 2 1s electrons influence
each other and shield the
pos. charge
The 2s electron experiences
the shielding by the 2 “inner”
electrons very strongly, but
not as full 2 neg. charges
41. CONSEQUENCE FOR ALL ELMENTS
As a result of penetration and shielding, the
order of energies in many-electron atoms is
typically
ns < np < nd < nf
because, in a given shell,
s orbitals are the most penetrating
and f orbitals are the least penetrating.