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Atomic structure 1
Important Atomic Models.
(1) Thomson's model
J.J. Thomson gave the first idea regarding structure of atom. According to this model.
(i) An atom is a solid sphere in which entire and positive charge and it's mass is uniformly distributed and
in whic
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2 Atomic Structure
Note : If t is the thickness of the foil and N is the number of D-particles scattered in a
particular direction ( T = constant), it was observed that constant .
After Rutherford's scattering of D-particles experiment, following conclusions were made as regard as
atomic structure :
(a) Most of the mass and all of the charge of an atom concentrated in a
very small region is called atomic nucleus.
(b) Nucleus is positively charged and it's size is of the order of 10–15 m | 1
Fermi .
(c) In an atom there is maximum e mpty space and the electrons revolve
around the nucleus in the same way as the planets revolve around the sun.
Draw backs
(i) Stability of atom : It could not explain stability of atom because according to classical electrodynamic
theory an accelerated charged particle should continuously radiate energy. Thus an electron moving in an
circular path around the nucleus should also radiate energy and thus move into
smaller and smaller orbits of gradually decreasing radius and it should
ultimately fall into n ucleus.
(ii) According to this model the spectrum of atom must be continuous
where as practically it is a line spectrum.
(iii) It did not explain the distribution of electrons outside the nucleus.
(3) Bohr's model
Bohr proposed a model for hydrogen atom which is also applicable for some lighter atoms in which a
single electron revolves around a stationary nucleus of positive chargeZe (called hydrogen like atom)
Bohr's model is based on the following postulates.
(i) The electron can revolve only in certain discrete non-radiating orbits, called stationary orbits, for
which total angular momentum of the revolving electrons is an integral multiple of
i.e. where n = 1, 2, 3,pal ……..=
quantum number
Princi
(ii) The radiation of energy occurs only when an electron jumps from one permitted orbit to another.
When electron jumps from higher energy orbit ( E1) to lower energy orbit ( E2) then difference of energies
of these orbits i.e. E1 –E2 emits in the form of photon. But if electron goes from E2 to E1 it absorbs the same
amount of energy.
Note : According to Bohr theory the momentum of an revolving in second orbit of atom
will be
For an electron in the n th orbit of hydrogen atom in Bohr model, circumference of orbit ;
where O = de-Broglie wavelength.
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Atomic structure 11
(iv) Mirror nuclei : Nuclei having the same mass number A but with the proton number ( Z) and neutron number
(A –Z) interchanged (or whose atomic number differ by 1) are called mirror nuclei for example.
(2) Size of nucleus
(i) Nuclear radius : Experimental results indicates that the nuclear radius is pr oportional to A1/3 , where A is the mass
number of nucleus i.e. , where R0 = 1.2 u 10–15 m = 1.2 fm.
Note : Heavier nuclei are bigger in size than lighter nuclei.
(ii) Nuclear volume : The volume o f nucleus is given by
(iii) Nuclear density : Mass per unit volume of a nucleus is called nuclear density.
where m = Average of mass of a nucleon (= mass of proton + mass of neutron = 1.66u 10–27 kg)
and mA = Mass of nucleus
Note : U is independent of A, it means U is same of all atoms.
Density of a nucleus is maximum at it's centre and decreases as we move outwards from the nucleus.
(3) Nuclear force
Forces that keep the nucleons bound in the nucleus are called nuclear forces.
(i) Nuclear forces are short range forces. These do not exist at large distances
greater than 10–15 m.
(ii) Nuclear forces are the strongest forces in nature.
(iii) These are attractive force and causes stability of the nucleus.
(iv) These forces are charge independent.
(v) Nuclear forces are non-central force.
Nuclear forces are exchange forces
According to scientist Yukawa the nuclear force between the two nucleons is the
result of the exchange of particles called mesons between the nucleons.
S - mesons are of three types–Positive S meson (S+ ), negative S meson (S –), neutral S meson (S0 )
The force between neutron and proton is due to exchange of charged meson between themi.e.
The forces between a pair of neutrons or a pair of protons are the result of the exchange of neutral meson S(o)
between them i.e. and
Thus exchange of S meson between nucleons keepsthe nucleons bound together. It is responsible for the nuclear
forces.
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14 Atomic Structure
It is found that the mass of a nucleus is always less than the sum of masses of it's constituent nucleonsni free state.
This difference in masses is called mass defect. Hence mass defect
'm = Sum of masses of nucleons–Mass of nucleus
^Zm p ( A Z)m n ` M ^Zm p Zm e ( A Z)m z ` M '
where m p = Mass of proton, m n = Mass of each neutron, m e = Mass of each electron
M = Mass of nucleus, Z = Atomic number, A = Mass number, Mc = Mass of atom as a whole.
Note : The mass of a typical nucleus is about 1% less than the sum of masses of nucleons.
(2) Packing fraction
Mass defect per nucleon is called packing fraction
'm MA
Packing fraction ( f ) where M = Mass of nucleus, A = Mass number
A A
Packing fraction measures the stability of a nucleus. Smaller the value
40
of packing fraction, larger is the stability of the nucleus.
30
(i) Packing fraction may be of positive, negative or zero value. 20
10
(iii) At A = 16, f o Zero
0
(3) Binding energy (B.E.) A > 240
–10
The neutrons and protons in a stable nucleus are held together by –20
nuclear forces and energy is needed to pull them infinitely apart (or the
same energy is released during ht e formation of the nucleus). This energy is called the binding energy of the nucleus.
or
The binding energy of a nucleus may be defined as the energy equivalent to the mass defect of the nucleus.
If 'm is mass defect then according to Einstein's massenergy relation
Binding energy = 'm c2 = [{ m pZ + m n(A Z)} –M] c2
(This binding energy is expressed in joule, because'm is measured in kg)
If 'm is measured in amu then binding energy = 'm amu = [{ m pZ + m n(A –Z)} –M] amu = 'm u 931 MeV
(4) Bind ing energy per nucleon
The average energy required to release a nucleon from the nucleus is called binding energy per nucleon.
Binding energy per nucleon
Binding energy per nucleon v Stability of nucleus
Binding Energy Curve.
It is the graph between binding energy per nucleon and total number of nucleons (i.e. mass number A)
Binding energy per
8.0 He 26Fe56
nucleon (MeV)
6.0
4.0 Li
2.0 H 2
0
56 100 150 200
Mass number A
(1) Some nuclei with mass number A < 20 have large binding energy per nucleon than their neighbour nuclei. For
example . Thesenuclei are more stable than their neighbours.
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22 Atomic Structure
(a) 4.4 MeV (b) 5.4 MeV (c) 5.6 MeV (d) 6.5 MeV
k1 k2
o o
Solution : (b) p1 p2
m 1 = 216 m2 = 4
M = 220
Q-value of the reaction is 5.5 eV i.e. k 1 k 2 5.5 MeV ……(i)
By conservation of linear momentum p 1 p2 2(216 )k 1 2(4 )k 2 k 2 = 54 k 1 ……(ii)
On solving equation (i) and (ii) we get k 2 = 5.4 MeV.
20
Example: 15 Let m p be the mass of a proton, m n the mass of a neutron, M1 the mass of a 10 Ne nucleus and M 2 the mass of a
40
20 Ca nucleus. Then [IIT 1998; DPMT 2000]
(a) M2 2M1 (b) M 2 ! 2M1 (c) M 2 2M1 (d) M 1 10(m n m p )
Solution : (c, d) Due to mass defect (which is finally responsible for the binding energy of the nucleus), mass of a nucleus
20
is always less then the sum of masses of it's con
stituent particles 10 Ne is made up of 10 protons plus 10
neutrons. Therefore, mass of 20
10 Ne nucleus M 1 10 (m p m n )
Also heavier the nucleus, more is he mass defect thus20 (mn m p ) M 2 ! 10(m p mn ) M1
or 10 (m p m n ) ! M 2 M 1
M 2 M1 10 (m p mn ) M 2 M 1 M 1 M 2 2M 1
Tricky example: 1
Binding energy per nucleon vs mass number curve for nuclei is shown in the figure. W, X, Y and Z
are four nuclei indicated on the curve. The process that would release energy is [IIT -JEE 1999]
Y
(a) Y o 2Z Binding energy
8.5 X
nucleon in
8.0 W
7.5
(b) W o X + Z MeV
5.0 Z
(c) W o 2Y
(d) X o Y + Z 30 60 90 120
Mass number of nuclei
Solution : (c) Energy is released in a process when total binding energy of the nucleus (= binding energy per
nucleon u number of nucleon) is increased or we can say, when total binding energy of products
is more than the reactants. By calculation we can see that only in case of option (c) this happens.
Given W o 2Y
Binding energy of reactants = 120 u 7.5 = 900 MeV
and binding energy of products = 2 (60 u 8.5) = 1020 MeV > 900 MeV
Radioactivity.
The phenomenon of spontaneous emission of radiatons by heavy elements is called radioactivity. The elements which shows thisphenomenon are called
radioactive elements.
(1) Radioactivity was discovered by Henery Becquerel in uranium salt in the year 1896.
(2) After the discovery of radioactivity in uranium, Piere Curie and Madame Curie discovered a new radioactive
element called radium (which is 10 6 times more radioactive than uranium)
(3) Some examples of radio activesubstances are : Uranium, Radium, Thorium, Polonium, Neptunium etc.
(4) Radioactivity of a sample cannot be controlled by any physical (pressure, temperature, electric or magnetic field)
or chemical changes.
(5) All the elements with atomic number ( Z ) > 82 are naturally radioactive.
(6) The conversion of lighter elements into radioactive elements by the bombardment of fast moving particles is
called artificial or induced radioactivity.
(7) Radioactivity is a nuclear event and not atomic. Hence electronic configuration of atom don't have any
relationship with radioactivity.
Nuclear radiatons
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Atomic structure 23
According to Rutherford's experiment when a sample of radioactive substance is put in a lead box and allow the
emission of radiation through a small hole only. Whe n the radiation enters into the external electric field, they splits into
three parts
– D-J -rays +
u
D -u J -rays
u u u
Magnetic
– + u u u u
–
– rays E-
+
+ u raysu u u E - u field
– + u u u urays u
rays
(i) Radiations which deflects towards negative plate are called D-rays (stream of positively charged particles)
(ii) Radiations which deflects towards positive plate are called E particles (stream of negatively charged particles)
(iii) Radiations which are undeflected called J-rays. (E.M. waves or photons)
Note : Exactly same results were obtained when these radiations were subjected to magnetic field.
No radioactive substance emits both D and E particles simultaneously. Also J-rays are emitted after the
emission of D or E-particles.
E-particles are not orbital electrons they come from nucleus. The neutron in the nucleus decays into
proton and an electron. This electron is emitted out of the nucleus in the form of E-rays.
Properties of D, E and J-rays
Features D- particles E - particles J - rays
1. Identity Helium nucleus or Fast moving electron Photons (E.M. waves)
doubly ionised helium
atom ( 2He4)
2. Charge + 2e –e Zero
3. Mass 4 m p (m p = mass of 4 m p me Massless
proton = 1.87 u 10–27
4. Speed | 107 m/s 1% to 99% of speed of light Speed of light
5. Range of kinetic energy 4 MeV to 9 MeV All possible values between Between a minimum
a minimum certain value to value to 2.23 MeV
1.2 MeV
6. Penetration power (J, E, 1 100 10,000
D) (Stopped by a paper) (100 times of D) (100 times of E upto 30
cm of iron (or Pb) sheet
7. Ionisation power ( D > E > J) 10,000 100 1
8. Effect of electric or Deflected Deflected Not deflected
magnetic field
9. Energy spectrum Line and discrete Continuous Line and discrete
10. Mutual interaction with Produces heat Produces heat Produces, photo-electric
matter effect, Compton effect,
pair production
11. Equation of decay
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24 Atomic Structure
Radioactive Disintegration.
(1) Law of radioactive disintegration
According to Rutherford and Soddy law for radioactive decay is as follows.
"At any instant the rate of decay of radioactive atoms is proportional to the number of atoms present at that insta nt"
i.e. . It can be proved that N = N0 e±Ot
This equation can also be written in terms of mass i.e. M = M 0 e–
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Atomic structure 25
t = 2(T1/2 ) 1 N0 N0 1 3
u (25%) (75%)
2 2 (2) 2 4 4
t = 3(T1/2 ) 1 N0 N0 1 7
u (12.5%) (87.5%)
2 (2) (2) 3 8 8
t = 10 (T1/2 ) N0 10 | 99.9%
§1·
10 ¨ ¸ | 0 .1 %
(2) ©2¹
t = n (N 1/2 ) N n
2
(2)
Useful relation
After n half-lives, number of undecayed atoms
(4) Mean (or average) life ( W)
The time for which a radioactive material remains active is defined as mean (average) life of that material.
Other definitions
(i) It is defined as the sum of lives of all atoms divided by the total number of atoms
i.e.
(ii) From slope of the line shown in the graph Slope = –O
i.e. the magnitude of inverse of slope of curve is known as mean life (W).
t
(iii) From
If of N 0 .
i.e. mean life is the time interval in which number of undecayed atoms ( N) becomes times or 0.37 times or 37% of
original number of atoms. or
It is the time in which number of decayed atoms ( N 0 –N) becomes times or 0.63 times or 63% of original
number of atoms.
(iv) From
i.e. mean life is about 44% more than that of half life. Which gives us W > T(1/2)
Note : Half life and mean life of a substance doesn't change with time or with pressure, temperature etc.
Radioactive Series.
If the isotope that result s from a radioactive decay is itself radioactive then it will also decay and so on.
The sequence of decays is known as radioactive decay series. Most of the radio
-nuclides found in nature are
members of four radioactive series. These are as follows
Mass number Series (Nature) Parent Stable and Integer Number of lost
product n particles
4n Thorium (natural) 52 D = 6, E = 4
4n + 1 Neptunium
(Artificial) 52 D = 8, E = 5
