Important Formulas: Atoms

# Important Formulas: Atoms | 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
? ? .

```

## Physics Class 12

105 videos|425 docs|114 tests

## FAQs on Important Formulas: Atoms - Physics Class 12 - NEET

 1. What is an atom?
Ans. An atom is the smallest unit of matter that retains the properties of an element. It consists of a nucleus containing protons and neutrons, with electrons orbiting around the nucleus.
 2. How many protons are in an atom?
Ans. The number of protons in an atom is equal to its atomic number, which is specific to each element. Protons carry a positive charge and determine the element's identity.
 3. What is the role of electrons in an atom?
Ans. Electrons are negatively charged particles that orbit the nucleus of an atom. They are involved in chemical reactions, bonding with other atoms to form molecules.
 4. How do you calculate the number of neutrons in an atom?
Ans. The number of neutrons in an atom can be calculated by subtracting the number of protons (atomic number) from the atomic mass. Neutrons are neutral particles found in the nucleus of an atom.
 5. Why is the structure of an atom important in chemistry?
Ans. The structure of an atom, including the arrangement of protons, neutrons, and electrons, determines its chemical properties and behavior. Understanding atomic structure is crucial in explaining the behavior of elements and their interactions in chemical reactions.

## Physics Class 12

105 videos|425 docs|114 tests

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