Important Formulas: Nuclei | Physics Class 12 - NEET PDF Download

 Page 1


MODERN PHYSICS
? Work function is minimum for cesium (1.9 eV)
? work function W = h ?
0
 = 
0
hc
?
? Photoelectric current is directly proportional to intensity of incident radiation.
( ? – constant)
? Photoelectrons ejected from metal have kinetic energies ranging from 0 to
KE
max
Here KE
max
 = eV
s
V
s
 - stopping potential
? Stopping potential is independent of intensity of light used ( ?-constant)
? Intensity in the terms of electric field is
I = 
2
1
?
0
 E
2
.c
? Momentum of one photon is 
?
h
.
? Einstein equation for photoelectric effect is
h ? = w
0
 + k
max
?
?
hc
 = 
0
hc
?
 + eV
s
? Energy ?E = 
) A (
12400
0
?
eV
? Force due to radiation (Photon) (no transmission)
When light is incident perpendicularly
(a) a = 1 r = 0
F = 
c
A ?
,   Pressure = 
c
?
(b) r = 1, a = 0
F = 
c
A 2 ?
, P = 
c
2 ?
(c) when 0 < r < 1 and a + r = 1
F = 
c
A ?
 (1 + r), P = 
c
?
(1 + r)
Page 2


MODERN PHYSICS
? Work function is minimum for cesium (1.9 eV)
? work function W = h ?
0
 = 
0
hc
?
? Photoelectric current is directly proportional to intensity of incident radiation.
( ? – constant)
? Photoelectrons ejected from metal have kinetic energies ranging from 0 to
KE
max
Here KE
max
 = eV
s
V
s
 - stopping potential
? Stopping potential is independent of intensity of light used ( ?-constant)
? Intensity in the terms of electric field is
I = 
2
1
?
0
 E
2
.c
? Momentum of one photon is 
?
h
.
? Einstein equation for photoelectric effect is
h ? = w
0
 + k
max
?
?
hc
 = 
0
hc
?
 + eV
s
? Energy ?E = 
) A (
12400
0
?
eV
? Force due to radiation (Photon) (no transmission)
When light is incident perpendicularly
(a) a = 1 r = 0
F = 
c
A ?
,   Pressure = 
c
?
(b) r = 1, a = 0
F = 
c
A 2 ?
, P = 
c
2 ?
(c) when 0 < r < 1 and a + r = 1
F = 
c
A ?
 (1 + r), P = 
c
?
(1 + r)
When light is incident at an angle ? with vertical.
(a) a = 1, r = 0
F = 
c
cos A ? ?
, P = 
A
cos F ?
 = 
c
?
 cos2 ?
(b) r = 1, a = 0
F = 
c
cos A 2
2
? ?
, P = 
c
cos 2
2
? ?
(c) 0 < r < 1, a + r = 1
P = 
c
cos
2
? ?
 (1 + r)
? De Broglie wavelength
? = 
mv
h
= 
P
h
 = 
h
2mKE
? Radius and speed of electron in hydrogen like atoms.
r
n
 = 
Z
n
2
a
0
a
0
 = 0.529 Å
v
n
 = 
n
Z
v
0
v
0
 = 2.19 x 10
6
 m/s
? Energy in nth orbit
E
n
 = E
1
 . 
2
2
n
Z
E
1
 = – 13.6 eV
? Wavelength corresponding to spectral lines
?
1
 = R 
?
?
?
?
?
?
?
?
?
2
2
2
1
n
1
n
1
for Lyman series n
1
 = 1 n
2
 = 2, 3, 4...........
Balmer n
1
 = 2 n
2
 = 3, 4, 5...........
Paschen n
1
 = 3 n
2
 = 4, 5, 6...........
? The lyman series is an ultraviolet and Paschen, Brackett and Pfund series
are in the infrared region.
? Total number of possible transitions, is 
2
) 1 n ( n ?
, (from nth state)
? If effect of nucleus motion is considered,
r
n
 = (0.529 Å)  
Z
n
2
 . 
?
m
E
n
 = (–13.6 eV) 
2
2
n
Z
 . 
m
?
Page 3


MODERN PHYSICS
? Work function is minimum for cesium (1.9 eV)
? work function W = h ?
0
 = 
0
hc
?
? Photoelectric current is directly proportional to intensity of incident radiation.
( ? – constant)
? Photoelectrons ejected from metal have kinetic energies ranging from 0 to
KE
max
Here KE
max
 = eV
s
V
s
 - stopping potential
? Stopping potential is independent of intensity of light used ( ?-constant)
? Intensity in the terms of electric field is
I = 
2
1
?
0
 E
2
.c
? Momentum of one photon is 
?
h
.
? Einstein equation for photoelectric effect is
h ? = w
0
 + k
max
?
?
hc
 = 
0
hc
?
 + eV
s
? Energy ?E = 
) A (
12400
0
?
eV
? Force due to radiation (Photon) (no transmission)
When light is incident perpendicularly
(a) a = 1 r = 0
F = 
c
A ?
,   Pressure = 
c
?
(b) r = 1, a = 0
F = 
c
A 2 ?
, P = 
c
2 ?
(c) when 0 < r < 1 and a + r = 1
F = 
c
A ?
 (1 + r), P = 
c
?
(1 + r)
When light is incident at an angle ? with vertical.
(a) a = 1, r = 0
F = 
c
cos A ? ?
, P = 
A
cos F ?
 = 
c
?
 cos2 ?
(b) r = 1, a = 0
F = 
c
cos A 2
2
? ?
, P = 
c
cos 2
2
? ?
(c) 0 < r < 1, a + r = 1
P = 
c
cos
2
? ?
 (1 + r)
? De Broglie wavelength
? = 
mv
h
= 
P
h
 = 
h
2mKE
? Radius and speed of electron in hydrogen like atoms.
r
n
 = 
Z
n
2
a
0
a
0
 = 0.529 Å
v
n
 = 
n
Z
v
0
v
0
 = 2.19 x 10
6
 m/s
? Energy in nth orbit
E
n
 = E
1
 . 
2
2
n
Z
E
1
 = – 13.6 eV
? Wavelength corresponding to spectral lines
?
1
 = R 
?
?
?
?
?
?
?
?
?
2
2
2
1
n
1
n
1
for Lyman series n
1
 = 1 n
2
 = 2, 3, 4...........
Balmer n
1
 = 2 n
2
 = 3, 4, 5...........
Paschen n
1
 = 3 n
2
 = 4, 5, 6...........
? The lyman series is an ultraviolet and Paschen, Brackett and Pfund series
are in the infrared region.
? Total number of possible transitions, is 
2
) 1 n ( n ?
, (from nth state)
? If effect of nucleus motion is considered,
r
n
 = (0.529 Å)  
Z
n
2
 . 
?
m
E
n
 = (–13.6 eV) 
2
2
n
Z
 . 
m
?
Here µ - reduced mass
µ = 
) m M (
Mm
?
,  M - mass of nucleus
? Minimum wavelength for x-rays
?
min
 = 
0
eV
hc
 = 
Å
) volt ( V
12400
0
? Moseley’s Law
v
 = a(z – b)
a and b are positive constants for one type of x-rays (independent of Z)
? Average radius of nucleus may be written as
R = R
0
A
1/3
, R
0
 = 1.1 x 10
–15
 M
A - mass number
? Binding energy of nucleus of mass M, is given by B = (ZM
p
 + NM
N
 – M)C
2
? Alpha - decay process
He Y X
4
2
4 A
2 z
A
Z
? ?
?
?
Q-value is
Q = ? ? ? ? ? ? ? ?
2 4
2
4 A
2 z
A
Z
C He m Y m X m ? ?
?
?
? Beta- minus decay
? ?
?
? ? ? ? ? Y X
A
1 z
A
Z
Q- value = 
2
A
1 Z
A
z
c )] Y ( m ) X ( m [
?
?
? Beta plus-decay
X
A
z
 ? ? ? Y
A
1 Z ?
 + ?+ + ?
Q- value = 
2
A
1 Z
A
z
c ] me 2 ) Y ( m ) X ( m [ ? ?
?
? Electron capture : when atomic electron is captured, X-rays are emitted.
X
A
z
 + e  ? ? ?  Y
A
1 Z ?
 + ?
Q - value  = 
2
A
1 Z
A
z
c )] Y ( m ) X ( m [
?
?
? In radioactive decay, number of nuclei at instant t is given by N = N
0
 e
– ?t
 ,
?-decay constant.
? Activity of sample : A = A
0
 e
– ?t
? Activity per unit mass is called specific activity.
? Half life : T
1/2
 = 
?
693 . 0
? Average life : T
av
 = 
693 . 0
T
2 / 1
Page 4


MODERN PHYSICS
? Work function is minimum for cesium (1.9 eV)
? work function W = h ?
0
 = 
0
hc
?
? Photoelectric current is directly proportional to intensity of incident radiation.
( ? – constant)
? Photoelectrons ejected from metal have kinetic energies ranging from 0 to
KE
max
Here KE
max
 = eV
s
V
s
 - stopping potential
? Stopping potential is independent of intensity of light used ( ?-constant)
? Intensity in the terms of electric field is
I = 
2
1
?
0
 E
2
.c
? Momentum of one photon is 
?
h
.
? Einstein equation for photoelectric effect is
h ? = w
0
 + k
max
?
?
hc
 = 
0
hc
?
 + eV
s
? Energy ?E = 
) A (
12400
0
?
eV
? Force due to radiation (Photon) (no transmission)
When light is incident perpendicularly
(a) a = 1 r = 0
F = 
c
A ?
,   Pressure = 
c
?
(b) r = 1, a = 0
F = 
c
A 2 ?
, P = 
c
2 ?
(c) when 0 < r < 1 and a + r = 1
F = 
c
A ?
 (1 + r), P = 
c
?
(1 + r)
When light is incident at an angle ? with vertical.
(a) a = 1, r = 0
F = 
c
cos A ? ?
, P = 
A
cos F ?
 = 
c
?
 cos2 ?
(b) r = 1, a = 0
F = 
c
cos A 2
2
? ?
, P = 
c
cos 2
2
? ?
(c) 0 < r < 1, a + r = 1
P = 
c
cos
2
? ?
 (1 + r)
? De Broglie wavelength
? = 
mv
h
= 
P
h
 = 
h
2mKE
? Radius and speed of electron in hydrogen like atoms.
r
n
 = 
Z
n
2
a
0
a
0
 = 0.529 Å
v
n
 = 
n
Z
v
0
v
0
 = 2.19 x 10
6
 m/s
? Energy in nth orbit
E
n
 = E
1
 . 
2
2
n
Z
E
1
 = – 13.6 eV
? Wavelength corresponding to spectral lines
?
1
 = R 
?
?
?
?
?
?
?
?
?
2
2
2
1
n
1
n
1
for Lyman series n
1
 = 1 n
2
 = 2, 3, 4...........
Balmer n
1
 = 2 n
2
 = 3, 4, 5...........
Paschen n
1
 = 3 n
2
 = 4, 5, 6...........
? The lyman series is an ultraviolet and Paschen, Brackett and Pfund series
are in the infrared region.
? Total number of possible transitions, is 
2
) 1 n ( n ?
, (from nth state)
? If effect of nucleus motion is considered,
r
n
 = (0.529 Å)  
Z
n
2
 . 
?
m
E
n
 = (–13.6 eV) 
2
2
n
Z
 . 
m
?
Here µ - reduced mass
µ = 
) m M (
Mm
?
,  M - mass of nucleus
? Minimum wavelength for x-rays
?
min
 = 
0
eV
hc
 = 
Å
) volt ( V
12400
0
? Moseley’s Law
v
 = a(z – b)
a and b are positive constants for one type of x-rays (independent of Z)
? Average radius of nucleus may be written as
R = R
0
A
1/3
, R
0
 = 1.1 x 10
–15
 M
A - mass number
? Binding energy of nucleus of mass M, is given by B = (ZM
p
 + NM
N
 – M)C
2
? Alpha - decay process
He Y X
4
2
4 A
2 z
A
Z
? ?
?
?
Q-value is
Q = ? ? ? ? ? ? ? ?
2 4
2
4 A
2 z
A
Z
C He m Y m X m ? ?
?
?
? Beta- minus decay
? ?
?
? ? ? ? ? Y X
A
1 z
A
Z
Q- value = 
2
A
1 Z
A
z
c )] Y ( m ) X ( m [
?
?
? Beta plus-decay
X
A
z
 ? ? ? Y
A
1 Z ?
 + ?+ + ?
Q- value = 
2
A
1 Z
A
z
c ] me 2 ) Y ( m ) X ( m [ ? ?
?
? Electron capture : when atomic electron is captured, X-rays are emitted.
X
A
z
 + e  ? ? ?  Y
A
1 Z ?
 + ?
Q - value  = 
2
A
1 Z
A
z
c )] Y ( m ) X ( m [
?
?
? In radioactive decay, number of nuclei at instant t is given by N = N
0
 e
– ?t
 ,
?-decay constant.
? Activity of sample : A = A
0
 e
– ?t
? Activity per unit mass is called specific activity.
? Half life : T
1/2
 = 
?
693 . 0
? Average life : T
av
 = 
693 . 0
T
2 / 1
? A radioactive nucleus can decay by two different processes having half
lives t
1
 and t
2
 respectively. Effective half-life of nucleus is given by
2 1
t
1
t
1
t
1
? ? .