1.1 Useful constants
electron charge=4.8x10-10 esu=1.6x10-19C
The atomic mass of C is 12.01 amu. What is the mass of 1 C atom? 1 C atom 6.02214 x 10 23 C atoms 1 mol C atoms x 1 mol C atoms x 12.011 g C = 1.9945 x 10-23 g C Molar Mass/Molecular Mass The molar mass of a molecule is simply the sum of the atomic masses. CH 4 = 1 mole C atoms + 4 moles H atoms 12.01 12.01 + 4 x 1.0079 + 4.0316. An element `X` of atomic mass `25.0` exists as `X4` in benzene to the extent of `100%`. When `10.30` g of saturated solution of `X` in benzene is added to `20.0` g of benzene, the depression in freezing point of the resulting solution is `0.51` `K.` If `Kf` for benzene is ` 5.1 K` `kg mol^(–1)`, find the solubility of `X` in `100` g of benzene. Since (1-x) = (1 - 0.996) = 0.004, multiply by 100: nitrogen-15 is 0.4%. The abundance of the nitrogen-14 isotope is 99.6 percent, and the abundance of the nitrogen-15 isotope is 0.4 percent. Calculating Relative Abundance in Mass Spectroscopy. This can be explained by atomic theory if the copper-to-chlorine ratio in the brown compound is 1 copper atom to 2 chlorine atoms, and the ratio in the green compound is 1 copper atom to 1 chlorine atom. The ratio of chlorine atoms (and thus the ratio of their masses) is therefore 2 to 1.
4x4 Magazine
electron mass= 9.1 x10-28gm
1.05 x10-27 ergs-s=6.58 x10-16 eV
Avogardro number= 6.022x1023 /mol
Boltzmann's constantk = 1.380658 x 10-23 J/K=8.617 x 10-5 eV/K
1.2.Energy conversion factors
1 eV = 8065.54 cm-1
1 a.u = 27.211396 eV = 219 474.63 05 cm-1 =2 Ry
1 Ry = 13.6057 eV
1 Ry = 13.6057 eV
1 degree kelvin=0.0862 meV(energy units for cold atoms)
= 0.695 cm-1
= 0.695 cm-1
1 Kcal/mol= 0.0434 eV = 43.4 meV(energy units used by chemists)
1 GHz in photon à 4.13x10-6 eV(energy units by laser physicists)
photon momentum (a.u.)k= 2.7 x10-4 E (eV)
de Broglie wavelengthfor electron:(in ;( at 100 eV is 1.22
1.3. Atomic units(au)e==m=1
Unit oflength=a0=Bohr radius=0.529(
Unit of velocity= = v0 = electron velocity in the first Bohr orbital= αc
(: fine structure const)
Unit of time = a0/αc= 24.2 asec(1 fs=41 au)asec=10-18 sec(attosecond)
Unit of frequency= v0 /a0= 4.13 x1016 sec-1
Unit of Electric field= 5.14x109 V/cm =e/a02
Unit of Magnetic field= 2.35 x105 tesla
Unit of magnetic dipole moment=Bohr magneton=µB=e/2m=5.79x10-5 eV/Telsa
Unit of electric dipole moment=ea0
1.4.Short hand notations
109=giga, 1012 =tera;1015= peta ;1018 =exa ; 1021=zetta ;1024=yocto
10-9=nano 10-12 =pico;10-15=femto; 10-18=atto;10-21=zepto;10-24=yotta
1.4. Lasers
For 1 oA, photon energy= 455.71 aufor 800 nm ->
laser peak intensity (linear polarized) =3.54 x1016 W/cm2
UP=E2/4=9.33 I(1014 W/cm2)(inm)
( 6eV for 800 nm at 1014 W/cm2)
Keldysh parameter
time-frequency width relation:
Atomic 1 0 4 X 4 Post Brackets
(is FWHM in time domain)
width in eV for a Gaussian pulse with is 1.83 eV
1.5. Oscillator strength and transition rates
A= 2*(E2/c3) f (4.13 x1016) 1/sec
where E is in a.u. , c=137.03604 and f is the oscillator strength for emission
1.6 pressure
1 atm=1.01x105 Pa= 760 Torr =1.013 bar
1 mbar= 0.75 Torr
1 psi= 51.7 torr = 0.068 atom
1.7. Binding energies and equilibrium distance
Kr: 14.0 eV, Xe: 12.3 eV
N2: 15.6 eV, 17.2 eV, 18.7 eVRO=1.10 A,N2+: 1.12A
![Atomic Atomic](https://www.researchgate.net/profile/Ari-Seitsonen/publication/27258578/figure/fig1/AS:310013286469634@1450924335413/The-atomic-coordinates-for-the-best-fit-model-of-c-2-4-2O-as-obtained-by-quantitative.png)
O2: 12.3 eV, 16.7 eV, 18.2 eVR0= 1.21 A,O2+: 1.12A
CO2: 13.8 eV, 17.6 eV, 18.1 eV