Download Mindfiesta Page 1 CHAPTER – 13 NUCLEI EXPERT`S TIPS : (1) An

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CHAPTER – 13
NUCLEI
EXPERT’S TIPS :
(1)
An atom has a nearly continuous mass distribution in Thomson’s atom model. But
according to Rutherford’s atom model, the distribution of mass in the atom is highly nonuniform.
(2)
Rutherford -scattering experiment established the existence of nucleus.
(3)
Distance of closest approach gives the estimate of the size of the nucleus.
(4)
The process of restricting the possible values of a physical quantity to a set of discrete
values is called quantization.
(5)
The radius of first orbits of hydrogen atom is called Bohr’s radius.
(6)
For hydrogen atom, the value of Rydberg’s constant,
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RH = 1.097  107 m-1
(7)
The spectral lines of Lyman series lie in ultraviolet region, those of Balmer series in visible
region and while those of Paschen series lie in infrared region.
(8)
The line emission spectrum is due to atoms, while the band emission spectrum is due to
the molecules of an element.
(9)
From the point of view of emission of characteristics X-rays, atomic number (and not the
atomic weight) is more fundamental.
(10) When the -particle is at the distance of the closest approach from a heavy mucleus, its
kinetic energy appears as the potential energy i.e.
Ep = E k
(11) The constant  =
1
2e
is called fine structure constant and its value is 1/137.

4ε  ch
(12) In terms of fine structure constant, velocity of the electron is nth orbit is given by
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νn = 
c
1
c


n 137 n
(13) If T1 and T2 are time periods of the electron in orbits of principal quantum numbers n1
and n2 respectively, then
T1 n13

T2 n23
(14) If RH is Rydberg’s constant for hydrogen atom, then
RH hc = 13.6eV
(15) The energy of the electron in nth energy state of the hydrogen-atom can be expressed as
En 
RHhc 13.6

eV
n2
n2
(16) The total energy of an electron in an orbit is equal to the negative of the negative of the
kinetic energy in that orbit.
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(17) The reciprocal of wavelength is called wave number and denotes the number of waves in
_
_
1 m. It is denoted by v . Thus, v =
1 c

λ v
(18) The series limit of any spectral series corresponds to ni = . It has maximum energy and
hence the shortest wavelength.
(19) If n is the quantum number of the highest energy level involved in the transitions, then
the total number of spectral lines emitted.
N=
n(n  1)
2
(20) Bohr’s theory of hydrogen atom is equally applicable to hydrogen-like atoms, such as
singly ionised helium (He+), doubly ionised lithium (Li++) atoms, etc.
For hydrogen-like atoms:
(a) Radius of nth atoms:
n2h2
rn  4ε0  2
4 mZe2
(b) Speed of electron in nth orbit:
1
2Ζe2
vn 

4e0
nh
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2
(c) Energy of electron in nth orbit:
 1  22mZ2e4
En   
 
n2h2
 4ε0 
(d) Energy of radiation emitted:
 1  22Z2e4 1
1
E
 2
 
2
2
h
nf
ni
 4ε  
2
(21) The energy of the electron in nth energy of the hydrogen – like atom can be expressed as
En 
RHhc
13.6
 Z2   2  Z2
2
n
n
(22) The wavelength of spectral lines emitted in hydrogen-like atom are given by
 1
1
1 
 RH Z2  2  2 
λ
ni 
 nf
(23) For K - like, ni = 2 and nf = 1 and for K - line, ni = 3 and nf = 1.
(24) The minimum wavelength of the X-rays produced is inversely proportional to the
accelerating voltage and is given by
min =
hc
eV
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(25) When the transition from the shell ni to the shell nf takes place, the frequency of the X-ray
emitted from the tanget (atomic number = Z) is given by
 1
1 
v = R c (Z – b)2  2  2  ,
ni 
 nf
where b is screening constant.
(26) Neutron is unstable particle outside the nucleus.
(27) The atoms, whose nuclei have same number of neutrons, are called isotones.
(28) The atoms, which have same mass number but different atomic numbers, are called
isobars.
(29) The atoms, whose nuclei have same difference in the number of neutrons and protons are
called isodiaspheres.
(30) Mass number is the integer closet to the nuclear mass.
(31) Nuclear density is same for all nuclei i.e. independent of the mass number of the nucleus.
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(32) The extremely large magnitude of electrostatic force of repulsion between protons is the
basic cause of nuclear instability.
(33) Nuclear forces are strongest attractive forces, which hold nucleons together inside the
nucleus. They are short range, charge independent and non-central forces.
(34) Nucleons ar bound together by the strong nuclear force. The binding energy of the
nucleus may be termed as the work done against the binding force to pull the nucleons
apart.
(35) The stability of a nucleus (in addition to a few other factors) depends upon binding energy
per nucleon rather than the total binding energy of the nucleus.
(36) The binding energy per nucleon has a low value for both very heavy nuclei. In order to
attain higher value of binding energy per nucleon, the lighter nuclei may unite together to
form a heavier nucleus (process of nuclear fusion) or a heavier nucleus may split into
lighter nuclei (process of nuclear fission).
(37) If R1 and R2 are the radii of the nuclei of mass numbers A1 and A2 respectively, then
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1/3
R1 R 0A11/3  A1 



R2 R 0A21/3  A2 
(38) The minimum separation energy required to remove a neutron from the nucleus ZXA is
equal to the binding energy of ZXA-1 nucleus and the neutron.
(39) Following conclusions can be drawn from the graph between B.E/A and A:
(a)
In the region A < 20, the B.E./A, of the nuclei is quite low except for the nuclei
2He
, 6C12 and 8O16. In an attempt to have grate value of B.E./A, the nuclei in the
4
region A < 20 unite of form a heavier nucleus and therefore, the nuclei in this
region are prone to nuclear fusion.
(b)
In the region A > 210, the B.E./A of the nuclei is again quite low. The nuclei in this
region have a tendency to split so as to improve the value of their B.E./A. Hence,
in region A > 210, the nuclei are prone to nuclear fission.
(c)
In the region 40 < A < 120, the nuclei are most stable. It is indicated by the flat
shape of the graph. The value of the B.E./A in this region is maximum ( 8.8 MeV
per nucleon).
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(40) This low value of binding energy per nucleon is case of heavy nuclei is unable to have
control over the Coulomb’s repulsion between the large number of proton. Such nuclei are
unstable and are found to undergo -decay.
(41) The neutron to proton ratio increases during -decay.
(42) The -decay leads to increase in Coulomb’s repulsive force, but it increase binding energy
per nucleon.
(43) The neutron to proton ration decreases during -decay.
-decay: It is represented by
A
ZX

Z-2Y
A-4
+ 2He4 + Q
-decay: it is represented by
A
ZX
-decay:

Z + 1Y
A
+
-1e
0
_
+ v +Q
When on  or -decay, the nucleus is left in excited state; the nucleus goes to
lower energy state or ground state by the emission of -ray (radiation of very short
wavelength.)
(44) The -particles are helium nuclei.
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(45) The electrons of nuclear origin are called -particles.
(46) The -rays are high energy photons of electromagnetic waves having extremely small
wavelengths.
(47) The total life of a radioactive sample is infinite.
(48) -ray spectrum is continuous in nature, while in -ray and -ray spectrum, the emitted
energy has only discrete values.
_
(49) The particle antineutrino ( v ) was postulated, so that spin conservation principle is not
violated in the process of nuclear electron-decay (- - decay). For the same reason,
particle neutrino (v) is essential for explaining the process of nuclear positron-decay (B+ decay).
(50) Due to the emission of -particle, mass number decreases by 4 and the atomic number
decreases by 2. On the other hand, due to the emission of -particle, mass number
remains unchanged but the atomic number increases by 1.
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(51) On passing through an absorbing material, the intensity of -radiatiation decreases
exponentially with the thickness traversed and is given by I = I0e-x, where  is absorption
coefficient of the absorbing material.
(52) The half-life of a radioactive sample is 0.693 times its mean-life i.e. T = 0.693 Ta
(53) After a time t (= n T), the fraction of the radioactive atoms left behind,
n
N 1
1
   
N0  2 
2
t/T
(54) After a time t (= n T), the fractional activity of a radioactive sample,
n
R
1
1
   
R0  2 
2
t/T
(55) When nuclear fission and fusion reaction occur, there is a decrease in nuclear mass in
both the cases.
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(56) In the fission reaction take place at high temperature, because kinetic energy to
overcome repulsion between the reacting nuclei. For this reason, fusion reactions are
known as thermonuclear reactions.
(57) The operation of a nuclear is said to be critical, when the multiplication factor (k)
approaches 1.
(58) In the fusion process, the energy released = binding energy of the product nuclei –
binding energy of the reacting nucleus
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