bohr1

Sheet1

physicsmatayom
Bohr_H_atom
content
note
1
mvr=n*hbar
1st_bohr;angularmomentum(mvr);hbar=h/(2*pi)
2
Delta(E)=Eni-Enf=hf
2st_bohr;line_spectra
3
FE=ke^2/r^2
coulomb_force
4
FC=mv^2/r
centripetal force
5
ke^2/r^2=mv^2/r
eq3&eq4
6
ke^2=mv^2r
eq3&eq4
7
mr*ke^2=(mvr)^2
eq3&eq4
8
mr*ke^2=(nh_bar)^2
from eq1
9
r=(nh_bar)^2/(mke^2)
orbital of electron in H_atom
10
r=r1*n^2
orbital of electron in H_atom
11
r1=(1*h_bar)^2/(mke^2)
bohr_radius
12
Ek=(1/2)mv^2=(1/2)ke^2/r
kinetic energy
13
Ep=-ke^2/r
potential energy
14
E=Ek+Ep
Total_energy
15
E=-(1/2)ke^2/r
Total_energy
16
E=-(1/2)ke^2*[mke^2/(nhbar)^2]
Total_energy
17
E=-(1/2)mk^2e^2/(n^2*hbar^2)
Total_energy
18
E=-|E1|/n^2
Energy level
19
E1=-(1/2)mk^2e^4/(1^2*hbar^2)
ground state energy
20
E1(J)=-2.17E-18
ground state energy
21
E1(J)=-13.6eV
ground state energy
22
1eV=1.6e-19J
1 electron volt
23
E=-|E1|/n^2=-13.6eV/n^2
Energy level
24
DE=hf=hc/l=E_ni-E_nf
2st_bohr;line_spectra
25
1/l=(1/hc)*(Eni-Enf)
2st_bohr;line_spectra
26
E_ni=-(1/2)mk^2e^2/(ni^2*hbar^2)
initial state energy
27
E_nf=-(1/2)mk^2e^2/(nf^2*hbar^2)
final state energy
28
1/lemda=(mk^2e^2/(hc*2*hbar^2)*(1/nf^2-1/ni^2)
emission line spectrum wavelength from ni--->nf
29
1/lemda=[mk^2e^2/(4p*c*hbar^3]*(1/nf^2-1/ni^2)
h=2*pi*hbar
30
1/lemda=RH*(1/nf^2-1/ni^2)
H_atom_line spectra series
31
RH=(mk^2e^2)/(4*pi*c*hbar^3)
Rydberge constant
32
RH=1.097E+07 m^-1
Rydberge constant
33
nf=1
Lyman series(ultraviolet)
34
nf=2
Balmer series(visible light)
35
nf=3
Paschen series(infrared)
36
nf=4
Brackett series
37
nf=5
Pfund series
c(m/s)
3.00E+08
speed of light
h
6.63E-34
planck's constant
hbar=h/(2*pi())
1.055E-34
J.s
m
9.10E-31
electron mass
k
9.00E+09
coulomb's constant
e
1.60E-19
electron chagre
r1(m)=hbar^2/(mk^2e^2)
5.31E-11
bohr_radius
part1Orbital
n
rn=ri*n^2
En(eV)=E1/n^2
1
5.31E-11
-13.60
2
2.12E-10
-3.40
3
4.78E-10
-1.51
4
8.50E-10
-0.85
5
1.33E-09
-0.54
part2 spectraseries
h(J.s)=
6.63E-34
J.s
c(m/s)=
3.00E+08
m/s
hc(J.m)=
1.99E-25
1eV=
1.60E-19
J
1m=
1.00E+09
nm
hc(eV.nm)=
1.24E+03
part2_table spectra series
Eni-Enf=hc/l
ni
nf
Eni(eV)=E1/n^2
Enf(eV)=E1/n^2
(Eni-Enf)eV
l(nm)=hc/(Eni-Enf)
series
2
1
-3.40
-13.60
1.02E+01
121.88
Lyman
3
1
-1.51
-13.60
1.21E+01
102.83
Lyman
4
1
-0.85
-13.60
1.28E+01
97.50
Lyman
5
1
-0.54
-13.60
1.31E+01
95.21
Lyman
6
1
-0.38
-13.60
1.32E+01
94.02
Lyman
7
1
-0.28
-13.60
1.33E+01
93.31
Lyman
8
1
-0.21
-13.60
1.34E+01
92.86
Lyman
9
1
-0.17
-13.60
1.34E+01
92.55
Lyman
10
1
-0.14
-13.60
1.35E+01
92.33
Lyman
100
1
0.00
-13.60
1.36E+01
91.42
Lyman
1000
1
0.00
-13.60
1.36E+01
91.41
Lyman
3
2
-1.51
-3.40
1.89E+00
658.12
Balmer series(visible light)
red
4
2
-0.85
-3.40
2.55E+00
487.50
Balmer series(visible light)
blue
5
2
-0.54
-3.40
2.86E+00
435.27
Balmer series(visible light)
blue
6
2
-0.38
-3.40
3.02E+00
411.33
Balmer series(visible light)
violet
7
2
-0.28
-3.40
3.12E+00
398.13
Balmer series(visible light)
violet
8
2
-0.21
-3.40
3.19E+00
390.00
Balmer series(visible light)
violet
9
2
-0.17
-3.40
3.23E+00
384.62
Balmer series(visible light)
violet
10
2
-0.14
-3.40
3.26E+00
380.86
Balmer series(visible light)
violet
100
2
0.00
-3.40
3.40E+00
365.77
Balmer series(visible light)
violet
1000
2
0.00
-3.40
3.40E+00
365.63
Balmer series(visible light)
violet
4
3
-0.85
-1.51
6.61E-01
1880.36
Paschen series(infrared)
5
3
-0.54
-1.51
9.67E-01
1285.40
Paschen series(infrared)
6
3
-0.38
-1.51
1.13E+00
1096.88
Paschen series(infrared)
8
3
-0.21
-1.51
1.30E+00
957.27
Paschen series(infrared)
9
3
-0.17
-1.51
1.34E+00
925.49
Paschen series(infrared)
10
3
-0.14
-1.51
1.38E+00
904.02
Paschen series(infrared)
100
3
0.00
-1.51
1.51E+00
823.40
Paschen series(infrared)
1000
3
0.00
-1.51
1.51E+00
822.66
Paschen series(infrared)
5
4