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Physics For you | december ‘16 7

Managing Editor
Mahabir Singh

Editor
Anil Ahlawat
(BE, MBA)

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Volume 24 No. 12 December 2016

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NEET | JEE Essentials 8

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Physics Musing Problem Set 41 70

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Crossword 85

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Page 40

Physics For you | december ‘16 45

Isobars : f �e atoms having same mass number
but di�erent atomic number.

Example : 31H and 2
3He, 17

37Cl and 16
37S

Isotones : f �e nuclides having the same number
of neutrons.

Example : 17
37Cl and 19

39K
Isomers : f Nuclei with same atomic number and
mass number but existing in di�erent energy
state.

Nuclear size : • �e number of protons and neutrons
per unit volume is approximately constant over the
entire range of nuclei.
i.e., A

R
4
3

3p
 constant

⇒ A ∝ R3 ⇒ R ∝ A1/3

R = R0A
1/3; R0 = 1.2 fermi = 1.2 × 10

�15 m

Nuclear density, f r =
Mass of nucleus

Volume of nucleus

=
×

mA

R A
4
3 0

3p
=

3
4 0

3

m
Rp

⇒ r ∝ A0

And r = 2.23 × 1017 kg m�3

F Binding Energy
�e loss in energy which is responsible for binding •
the nucleons together in a nucleus is called the
binding energy.

Eb = DMc
2 where, DM = mass defect

DM = [ZmP + (A � Z)mN] � M
M → mass of nucleus

\ Eb = [(ZmP + (A � Z) mN)�M] × c
2



Binding energy per nucleon, • DE
E
Ab n

b
/ =

= Average energy needed to separate a nucleus into
its individual nucleons.
Shape of BE/ • A is determined primarily by three
factors

a constant term, which originates because f
nucleons interact only with their nearest
neighbours.
a sharp decrease for light nuclei. f
a gradual decrease for heavy nuclei due to f
coulomb repulsion of the nuclear protons.

Observation from the BE/ • A graph, energy can be
liberated in two di�erent ways

Nuclear fission : f A heavy nucleus breaks in
two light nuclei of comparable masses. BE per
nucleon is greater for two lighter fragments
than it is for the original nucleus.
Nuclear fusion : f Two light nuclei combine
to form a heavier nucleus. BE per nucleon is
greater in the �nal nucleus than it is in the two
original nuclei.

F Law of radioactive Decay
Rate of decay of nuclei is given by •

− ∝ ⇒ = −
dN
dt

N t
dN
dt

N t( ) ( )l
l → disintegration (decay) constant

Number of undecayed radioactive nuclei at any •
time t

N(t) = N0 e
�lt

N0 → number of nuclei at time t = 0
Number of decayed nuclei, •

Nd = N0 (1 � e
�lt)

t

N

N0 N0

Nd

t

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48 Physics For you | december ‘16

Mean life = Average life = • τ
lav

=
1

Half life = • T av1 2
2 0 693

0 693/
ln .

.= = =
l l

τ

Also, f τ
lav

T= =
1

1 44 1 2. /

Number of nuclei present after • n half life (t = nT1/2)

=
N

n
0

2( )


N

N N N Nt t t t
n0

0 0
2

0
3

01 2 1 2 1 2 1 2

2 2 2 2
/ / / /.... →  →  →  →

If a nuclide can decay simultaneously by two •
different processes with different decay constants
l1 and l2, then effective decay constant of the
nuclide is, l = l1 + l2 ; and N = N0 e

–(l1 + l2)t

Activity of sample: •



R
dN
dt

N N e

R e

t

t

= − = =

=





l l l

l

0

0

Here, R0 = lN0 is decay rate at t = 0.
Units of activity f

1 curie = 1 Ci = 3.7 × 1010 dps
1 Rutherford = 1 rd = 106 dps

1 Becquerel = 1 Bq = 1 dps

Alpha decay : • It is spontaneous decay of a heavy
nucleus by emitting an alpha particle.

Z
A

Z
AX Ya− −

− → +decay He+ 2
4

2
4 Q

Q f value of a-decay : Q = (mX – mY – mHe)c
2

This energy is shared by the daughter nucleus
and the alpha particle.

The energy released during the alpha decay of f

92
238U is 4.25 MeV.

The energy supplied to emit proton from f 92
238U

is 7.68 MeV. Hence a proton cannot be released
by 92

238U without supply of external energy.
Beta decay : • It is spontaneous decay of nucleus by
emitting an electron or a positron.

b u ub− − + −→ + +  → + +


decay : ;n p e X Y eZ
A

Z
A
1 1

0 f

b u ub+ + − +→ + +  → + +
+

decay : ;p n e X Y eZ
A

Z
A
1 1

0
f

The mass number f A of a nuclide undergoing
beta decay does not change.

Gamma decay : • It is the phenomenon of emission
of one or more g-ray photon by a nucleus in its
excited state so as to acquire its ground state.

Co

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Physics For you | DECEmbEr ‘16 85

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ACROSS
2. An instrument for measuring changes in

magnetic flux. [9]
3. A semiconductor device that acts as a

storage location in processing unit of a
computer. [8]

8. A unit of frequency equal to 1012 hertz.
[7]

11. A mechanical device that prevents any
sudden or oscillatory motion of a moving
part of any piece of apparatus. [4, 3]

12. A device used for separating two isotopes
by thermal diffusion. [7, 6]

15. An inductor that presents a relatively high
impedance to alternating current. [5]

17. An electronic instrument for measuring
very short time intervals. [11]

20. A particle made from glass is being
developed that can absorb pollutants from
contaminated water. [7, 8]

22. The path that a moving object follows
through space as a function of time. [10]

23. An equation that predicts the degree of thermal ionization
in a gas. [4, 8]

24. The variable voltage dividers with a shaft or slide control for
setting the division ratio. [13]

25. A machine invented by E.O. Lawrence in 1934. [9]
26. The process of boiling or bubbling up of a liquid. [10]
27. The forces which act on a solid object in the direction of the

relative fluid flow velocity. [4]
28. The reciprocal of the force constant. [10]
DOWN
1. Father of electrodynamics. [5, 5, 6]
4. A spinning wheel in which the axis of rotation is free to

assume any orientation by itself. [9]
5. An electrical device permitting only one way current flow.

[5]
6. A mode of computer processing and output in which a large

proportion of the output is in pictorial form. [8]
7. A part of the electromagnetic spectrum comprising low

energy X-rays. [5, 4]

9. A highly magnetized, rotating neutron star that emits a
beam of electromagnetic radiation. [6]

10. An electronic device in which a single bit of data is stored
temporarily. [5]

13. A rule for determining the direction of lines of magnetic
force around a wire carrying a current. [9, 4]

14. An instrument for measuring the inclination of a surface to
a horizontal plane. [12]

15. The special arrangement of molecules in a liquid crystal.
[9]

16. An optical system that produces a beam of parallel
light. [10]

18. The reciprocal of capacitance. [9]
19. An instrument for measuring optical transmission or

reflection of a material. [12]
21. An instrument that measures the rate of flow of fluids. [9]
25. The streams of gas and dust surrounding the nucleus of a

comet. [4]

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86 Physics For you | DECEmbEr ‘16

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