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atomic structure (Autosaved) .pdf


Original filename: atomic structure (Autosaved).pdf
Author: GAURAV

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Rutherford model:
Rnucleous = r0 (A) 1/3 ,[r0 = 1.4 x 10-15 m]
N(θ) = Ni n L Z2 k2 e4 / ( 4 r2 KE2 Sin4(θ/2)

Particle
electron
proton
neutron
Alpha (He+2)

Ni = no. of incident alpha particle
n = atoms per unit volume in target
L = thickness of target
r = target to detector distance

Mass (kg)
9.1 x 10-31 = 1/1837 amu
1.67 x 10-27 = 1.007 amu
1.67 x 10-27 = 1.008 amu
4 amu

Angular momentum of orbit = mvr = nh/2ᴫ
Force balance: kq1q2 /r2 = kze2/r2 = mv2/r
r = 0.529 n2 /z Ȧ
v = 2.18 x 106 z/n m/s
E = -13.6 z2/n2 ev = -2.18 x 10-18 z2/n2 J
K.E = -T.E
P.E = 2 T.E
T = 1.524 x 10-16 n3/z2
ν = 0.65 X 1016 z2/n3
Closest distance of approach: [ K.E. = P.E. ]
kq1q2 /r = ½ mv2

ΔE = En2 – En1 = h ν = hc/λ = hcū
ΔE = 13.6 Z2 ( 1 / n12 - 1 / n22 ) eV
ΔE = 2.18 x 10-18 Z2 ( 1 / n12 - 1 / n22 ) J

Number of spectral lines between
two level: = (n2 – n1) (n2 – n1 + 1)/ 2

ΔE = I.E. ( 1 / n12 - 1 / n22 )
1/ λ = ν/c = ū = R Z2 ( 1 / n12 - 1 / n22 )
R = 1.1 x 107 m-1

Bohr model:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.

Rydberg equation:

Charge (C)
-1.6 x 10-19
+1.6 x 10-19
0
2 x 1.6 x 10-19

Atomic
Structure

Series
lyman
balmer
paschen
Bracket
pfund
Humphery

transition
To n=1 from n = 2,3....
n=2
n=3
n=4
n=5
n=6

region
UV
VISIBLE (for H atom)
IR
IR
IR
IR

Debrolglie wave
λ = h/p = h/mc = h/mv = h/ √(2 m KE) = h/ √(2 m q V) = 2ᴫr/n
For electron, if accerlated through a potential difference of V
λe = h/ √(2 m e V) = 12.3 / √V = √(150/V) Ȧ

Photoelectric effect:
Plank quantum theory:
c = ν λ or ν = c ū

Unit conversion:

Heisenberg uncertainty principle:

ū = 1/ λ

1 Ȧ = 10-10 m
1 nm = 10-9 m
1 pm = 10-12m
1 amu = 1.67 x 10-27 kg
1 eV = 1.6 x 10-19 J
1 erg = 10-7 J
1 cal = 4.18 J

ΔX ΔP ≥ h/4ᴫ

Ephoton = hν = hc/λ = hcū = 1
quantum (energy of single
photon)
Etotal = n hν = n hc/λ = n hcū
(n is no. of quanta or photons)

ΔX ΔV ≥ h/4ᴫm
ΔE Δt ≥ h/4ᴫ
ΔX Δλ ≥ λ2 / 4ᴫ
Percentage error in position = ΔX/X x 100

hν = hc/λ= w0 + K.E
w0 = hν0 = hc/λ0
KE = eV (V is stopping potential)
Photo current = i = Q/t = ne/t (n is no. of ejected
photo electron)
I1 / I2 = i1 / i2 = (r2/r1)2 [ I = intensity, i =
photocurrent, r is distance between source and
metal surface ]


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