Atoms and Nucleus Notes and MCQs

Notes 35 Pages

Joint Entrance Examination (Main)

Physics

Contributed by

Gulzar Dubey

286
SUMMARY
1 The distance of the closest approach of an

- particle is given by
2
o K
.
1 2Ze
γo=
4π E E
where E
k
=
2
1
m
2

9 Z = Atomic number
2. The Impact parameter is given by
 
2
θ
2
2
o
2Ze Cot
1
b =
4π.E
m

3 No - of Scattering of

- particle reattered at angle

is given by
 
2
o
2 4
Ζe 1
N = N ns
m sin θ/2

where, No = number of incident

- particles
n = no. of Atoms per unit Volume in the foil
s = thickness of foil
v = speed of

- particle,m = mass of

particle
z = Atomic number of (the element of foil)
e = charge of electron.
4 Angular momentum of electron in Bohr orbit
2
nh
mvr


, whre n is an integer
5 r
n
= radius of n
th
bohr orbit =
2 2
2
n h o
Ze m


r
n
2
n
Z

6 Energy of electron in n
th
orbit is

4 2 2
n
2 2 2
2
o
me z z
E 13 . 6 ev
n n
8h
 
   
 

 
2
n
2
Z
E
n

7. different spetral Series Formula for and their gegionls
(i) Lyman series,
2 2
1 1 1
R where, n 2,3....
1 n
 
  
 

 
(ultra violet region.)
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287
ii) Balmer series, ,
2 2
1 1 1
R where, n 3, 4
2 n
 
  
 

 
,........
(Visible region.)
(iii) Paschen series, ,
2 2
1 1 1
R where, n 4,5
3 n
 
  
 

 
,........
(Infrared region.)
Braket series,
2 2
1 1 1
R where, n 5, 6
4 n
 
  
 

 
,........
(Infrared region.)
Pfund series,
2 2
1 1 1
R where, n 6, 7
5 n
 
  
 

 
,........
(Infrared region.)
8 For, hydrogen atom energy of electron in n
th
orbit
n
2
13.6
E eV
n
 
For hydrogen like atom
2
n
2
13.6
E =- z eV
n
9
A A
Z Z
X or X
Z = Atomic number = Number of Protons
A = mass number = Number of neucleons
A - Z = N = Number of neutrons
(i) For Isotope nuclei
Z equal and A unequal
e.g.
6
c
12

6
c
13

6
c
14
(ii) For, Isotone nuclei
Z unequal, A unqual
A-Z = N = equal
No - of neutrons are equal
e.g.
86 87
kr Rb
36 ,37
(iii) For, Isobar nuclei
z unequal , A equal
(A-Z) are unequal
e-g
12 12
5 6
B , C
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288
(iv) For Isomers nucler
Z equal, A equal
But their radio active properies are different
e.g.
80
35
Br
pair
10 Radius of nucleus R = Ro (A)
1
3
Where R
o
= Constant
= 1.1 fm to 1.2 fm
A = mass number
11 Mass defect
MNmnzmm
p
 )(
12 B.E
 
2 2
b
E ( m)c Zmp Nmn) M c    
13 Unit of energy in nuclear Physics or atomic Physics is eV
19
1eV 1.6 10 J

 
14 unit of mass in nuclear physics or atomic Physics is amu or u
27
1amu 1u 1.67 10 Kg

  
6
1u 931.48MeV 931.48 10 eV  
15 B.E Per nucleon is
n
b
b
E
E
A

16

- Particle = Nucleus of Helium atom
Symbol of

- Particle
4
2
He
 - Paricle = electron emitted From nucleus i
eo
γ
- radiation = photon. Symbol
γ
 - particle




or
e
1

or electron


Particle




or
e
1

or positron.
n

p +
e

 
n e

   
Where

Anti neutrino


neutrino
(17) unit of Radio activity
1 Bq = 1 disinteglation/s
1 curie = 3.7

10
10

disinteglation/s
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289
(18) Activity
dn
I N
dt
  
number of Atoms or nucler in a Radio active sample after time is given by
t
N N o e
 

Where

is radio active decay Constant
Activity I =
t
Io e

Mass
t
m mo e


(19) Half life
1
2
0.693
T 

Mean life
T
1


1
2
T 0.693T
Or
1
2
T 1.44 T
(20) In

- deccay Z decreasc by 2 and mass number A decrease by 4
In
β
- deccay Z increase by 1 and mass number does not change
In


deccay Z decrease by 1 and mass number does not change
In emission of r - ray or photon, Z and A does not change.
(21) Nuclear Fission.
The spiliting of a heavy nucleus into two or more fragments or moderate and
comparable sizes is called nuclear Fission
e.g
235 141 92 1
q2 56 36 O
U Ba Kr 3 n energy   
(22) Nuclear fusion.
The Process of nuclear fusion consists in the combination of two light nuclei to
form steble nucleus of mass less than the total intial mass.
1 1 2
1 1 1
1 2 3
1 1 2
3 3 4 1 1
2 2 2 1 1
H H H e
H H He
He He He H H

    
   
   
If any Q > 0 Exoergic
Q < 0 Endoergic
In any nuclear reactions consveration of momentum, charge and energy is must.
(23) Nucler reaction A (a,b) B or A+a

B + b + Q
A = Target Nucleus
a = Projected Particle
B = resulting (product) nucleus
b = emitted Particle
Q = energy equal muss defect
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290
MCQ
For the answer of the following questions choose the correct alternative from
among the given ones.
(1) In each of the following question match column -I and column -II select correct
Answer.
(A) Bohr atom model (P) fixed for the atom
(B) Ionisation potential (q) Nucleus
(C) Rutherford atom modal (r) stationary orbits
(D) Thomson atom modal (s) In atom positive and Nagative
charge are distrited uniformely.
(A) a

s , b

r , c

q , d

p
(B) a

r , b

p , c

q , d

s
(C) a

p , b

r , c

s , d

q
(D) b

p , c

q , b

r , d

s
(2) Read the following question and choose correct Answer form given below.
(A) Both assertion and reason are true. Reason is the correct explanation of the
Assertion
(B) BOth assertion and reason are true. Reason is not correct explanation of the
assertion
(C) Assertion is true but reason is false.
(D) Both Assertion and Reason are false
(i) Assertion :- In a radio-active disintegration, an election is emitted by nucleus.
Reason :- eleccon are always Present in-side the nucleus.
(ii) Assertion :- An election and Positon can annibilate each other creating Photon
Reason:- Electon and Positon form a Particle and anti Particle.
(iii) Assetion:- An isolated radioactive atom may not decay at all what eVer be its
half time
Reason:- Readioactive decay is a statistical Phenomena.
(iv) Assertion :- Fragment Produced in the fission of u
235
are active
Reason:- The fragments have abnormally high Proton to neutron ratio
(3) Each of the following question contain two stalements.choose correct answer
form the given below.
(i) statement-I:- Large angle scattering of al-pha Particle led to discovery of
atomic nucleus.
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291
state ment-II :- Entire Positive charge of atom is concentrated in the central core.
(A) statement -I and II are true. and statement II is correct explanation of
statement-I
(B) statement -I and II are true, but statement-II is not correct explanation of
statement I
(C) statement I is true, but state ment II is false.
(D) statement I is false but statement II is true
(ii) statement-I 1 amu=931.48 MeV
statement-II It follows form E=mc
2
(iii) statement -I:-half life time of tritium is 12.5 years
statement-II :- The fraction of tritium that remains after 50 years is 6.25%
(iv) statement-I:- Nuclei of different atoms have same size
state m ent-I I :- R
=Ro(A)
1
/
3
(4) Match column I and II and chose correct Answer form the given below.
(a) Nuclear fusion (p) converts some matter into energy
(b) Nuclear fission (q) generally Possible for muelei low atomic number
(c)

decay (r) generally Possible for ndcler high atomic number
(d) Exothermic nuclear (s) Eessentially Proceeds by weak nuclear for(c)
reaction
(A) a

p , b

r , c

d , d

q
(B) a

d , b

r , c

p , d

a
(C) a

q , b

r , c

d , d

p
(D) a

r , b

a , c

p , d

a
(5) A radioative sample has n
o
active atom at t=o, at the rate of dissntegration at any
time is R and the number of atom is N, then ratio.
R
N
 
 
 
varies with time (t) as.
(A)
t
R
N
(B)
t
R
N
(C)
t
R
N
(D)
t
R
N
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292
(6) The transition the state n=4 to n=1 in a hydrogen like atom results in ultraviolet
radiation. Infrared radition will be obtained in the transition form
(A) 3

2 (B) 5

4 (C)4

2 (D) 2

1
(7) In Bohr model the hydogen atom, the lowest orbil corresponds to
(A) Intinite energy (B) zero energy
(C) The minimum energy (D) The maximum energy
(8) Energy leVels A , B , C of a certain atom corresponding values of energy i.e
A B c
E E E 
If

1 2 3
, ,  
are wave lengths of radition corresponding to the
transition C

B , B

A and C

A. which of the following is correct
(A)
2 2 2
3 1 2
   
(B)
3 1 2
   
(C)
1 2
3
1 2
 
 
 
(D)
1 2 3
o   
(9) According to Bohr's theory the radius of electon in an orbit described by Principal
quantum number n and atomic number Z, is Proportional to.
(A)
2 2
Z n
(B)
2
n
Z
(C)
2
Z
n
(D)
2
2
n
z
(10) The energy of electron in the n
th
orbit of hydogen atom is expressed as
n
2
13.6
E ev
n
 
The shortest and longest wave length of lyman series will be.
(A)
o o
910A , 1213A
(B)
1315 A ,1530 A
 
(C)
5463A ,7858 A
 
(D) None of these
(11) Number of spectral lines in hydrogen atom is.
(A) 6 (B) 8 (C) 15 (D)

(12) In the nuclear reaction
7
3
X ( , ) Li 
the atom X will be
(A)
4
2
He
(B)
11
5
B
(C)
10
5
B
(D)
9
5
B
(13) The nucleus which has radius one third of the radius of
189
Cs
is
(A)
9
Be
(B)
19
F
(C)
12
C
(D)
7
Li
(14) A nucleus of
210
84
Po
originally at rest emits

-particle with speed v what will be
the recoil speed of the daughter nucleus
(A)
214

(B)
4
214

(C)
4
206

(D)
206

Page 7
293
(15) It the radius of a nucleus of mass number 3 is R. then the radius of a nucieus of
mass mumber 81 is
(A) 27 R (B) 9 R (C) 3 R (D)
 
1
2
27 R
(16) The nucler of which of following Pairs of nuclei are isotones
(A)
74 71
34 31
Se , Ca
(B)
92 92
42 40
Mo , Zr
(C)
81 86
38 38
Sr , Sr
(D)
40 32
20 16
Cd , S
(17) An electron change its Position from orbit n=4 to the orbit n=2 of an atom the
wave length of emitted radition in the form of R (where R is Redburg constanst)
(A)
16
7R
(B)
16
R
(C)
16
3R
(D)
16
5R
(18) The control rod in a nuclear reactor is made of
(A) uranium (B) Cadmium (C) plutomium (D) grabhite
(19) which of the following isotopes normally fissonable
(A)
233
92
U
(B)
238
92
U
(C)
235
92
U
(D)
239
93
Np
(20) which of the following statement is true
(A)
192
78
Pt
has 78 neutrons (B)
234 234 4
90 91 2
Th Pa He 
(C)
238 234 4
92 90 2
U Th He 
(D)
84
214 210
82
Po Pb

 
(21) A Free neutron decays into a Proton, an electron and
(A)

(B)

(C)

(D)

(22) The distance of the closest abbroach of an alpha particle fired at a nuclous with
kinctic energy K is ro. The distemce of the closest approach when thw

-
particle is fired at the same nucleus with kinetic energy 2k will be.
(A)
o
r
2
(B) 4r
o
(C)
o
r
4
(D) 2r
o
(23) which of the following series in the spectrum of hydrogen alon lies in the visible
legion of the electro magnetic spectrum?
(A) Paschen (B) Lyman (C) Brakett (D) Balmer
(24) If 13.6 eV energy is required to ionige the hydrogen aton the energy required to
remove the electron form n=2 state is
(A) Zero (B) 10.2 eV (C) 6.8 eV (D) 3.4 eV
Page 8
294
(25) It N
o
is the original mass of the substance of halt lift 5 years, the amount of
substance left after 15 years is
(A)
o
N
16
(B)
o
N
8
(C)
o
N
4
(D)
o
N
2
(26) when u-238 nucleus originalluy at lest decay by emitting an

-particle having a
speed u the recoil speed of the resi-dual nucleus is.
(A)
4u
238
(B)
4u
238

(C)
4u
234
(D)
4u
234

(27) At a certain instant, a radioactive sample has a decay rate of 5000 dis-interation
Per minute. After 5 minuter the decay rate is 1250 dis-interations Per minute.
Then the decay constant is (Per-min )
(A) 0.2 ln 4 (B) 0.4 ln 4 (C) 0.4 ln 2 (D) 0.8 ln 2
(28) A nucleus with Z=92 emits the following sequence
, , , , , , , , , , , , ,
     
             
The Z of the resulting nucleus is
(A) 76 (B) 78 (C)74 (D) 82
(29) which of the following can not be emitted in radioactive decay of the substance?
(A) Helium-nucleus (B) Electrons (C) Neutrions (D) Proton.
(30) It the radius of
27
13
Al
nucleus is 3.6 fm the radius of
125
52
Te
nucleus is nearly equal to
(A) 8 fm (B) 6 fm (C) 4 fm (D) 5 fm
(31) which of the following atom has the lowest ionization potentical?
(A)
14
7
N
(B)
40
18
Ar
(C)
133
55
cs
(D)
16
8
O
(32) If the binding energy of electron in a hydrogen atom is 13.6 eV, the energy
required to remove the elecron form the first state of Li
2
+
is.
(A) 13.6 eV (B) 30.6 eV (C) 122.4 eV (D) 3.4 eV
(33) The ionigation Potential of hydrogen atom is 13.6 eV. An electron in the ground
state absords Photon of energy 12.75 eV. How many dirrerent spectral lines can
one expect when electron make a down ward transition
(A) 1 (B) 2 (C) 6 (D) 4
(34) A radio-active nucleus
A
Z
X
emits 3

-particles and 2 Positrions. the ratio of
number of neuleuons to that of Protons in the final nucleus will be
(A)
A Z 8
Z 4
 

(B)
A Z 12
Z 4
 

(C)
A Z 4
Z 8
 

(D)
A Z 4
Z 2
 

Page 9
295
(35) An

-particle of energy
2
1
mv
2
bombards by a heavy nuclear target of charge ze.Then
the distance of closet approach for the alpha nucleus will be Probprtional to
(A)
3
1
Z
(B)
4
1

(C)
1
m
(D)
2
1

(36) when
7
3
Li
nucler are bombarded by Proton and the resultant nuclei are
8
4
Be
, the
emitted particle will be
(A) neutron (B) gamma (C) alpha (D) Beta
(37) starting with a samble of Puer cu-66,
7
8
of it decays into Zn, 15 minules the left
of the samble is
(A) 5 min (B) 7.5 min (C) 10 min (D) 15 min
(38) An

-particle of energy 5 MeV is scattered though
180

by a fixed uranium
nucleus. The distance of the closest approach nucleus The distance of the closest
approach is of the order of
(A)
8
10 cm

(B)
12
10 cm

(C)
10
10 cm

(D)
15
10 cm

(39) The binding energy Per nucleon of deutron
 
2
1
H
and Lielium nucleus
 
4
2
H e
is
1.1 MeV and 7.0 MeV.resbectively. If two beutron nucler react to form a single
helium nucleus, the energy released is
(A)23.6 MeV (B) 26.9 MeV (C) 13.9 MeV (D) 19.2 MeV
(40) The nucleus at rest disintegrate into two nuclear parts which have their velocities
in the ratio 2:1 The ratio of their nuclar sizes will be
(A)
3 2 :1
(B)
1:3 2
(C)
3 :1
(D)
1: 3
(41) A radiation of energy E falls normally on a Pertect reflecting surface. The
momentum transterred to the surtace is.
(A)
E
c
(B)
2E
c
(C)
2
E
c
(D) Ec
(42) In the following nuclear fusion reaction
2 3 4 1
1 1 2 o
H H He n  
the repalsive potential energy between the two fusing nucler is
14
7.7 10 J


The
Temperature to which the gas must be heated is nearly (Boltzman constmt
K=
23 1
1.38 10 JK
 

)
(A)
3
10 K
(B)
5
10 K
(C)
7
10 K
(D)
9
10 K
Page 10

Atoms and Nucleus Notes and MCQs

Atoms and Nucleus Notes and MCQs

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