ATOMIC NUCLEUS

Q.1 In a head on collision between an  particle and gold nucleus (Z = 79), the
closest distance of approach is 41.3 fermi. Calculate the energy of  particle.
(5.51 MeV)
Q.2 Find the energy of hydrogen atom in its ground state and in the energy levels
whose quantum number are 2 and 3. (-13.6 eV, -3.4 eV, -
1.51 eV)
Q.3 Find the energy radiated in the Lyman series of hydrogen atom spectrum when
its electron jumps from 3rd energy level to ground state.
Q.4 Determine the longest wavelength in Lyman series of hydrogen spectrum.
(1210 Å)
Q.5 The total energy of electron in the first excited state of hydrogen atom is about -
3.4 eV. (a) What is the kinetic energy of electron this state? (b)
What is the potential energy of electron this state? (c) Which of the K.E., P.E. or
total energy will change if the choice of zero reference of potential energy is
changed? (3.4 eV, -6.8 eV, P.E. & T.E.)
Q.6 What is the ground state energy of electron in case 3Li7? (-
30.4 eV)
Q.7 Find the ratio of radii of two nuclei with mass numbers 1 and 27 respectively.
(1:3)
Q.8 Two nuclei have radii in the ratio 1:8, what is ratio of their nuclear densities and
mass numbers?
Q.9 The half life of a radioactive substance is 30 days. What is the time taken for 3/4 th
of its original mass to disintegrate?
Q.10 The half life of a radioactive substance is 1.192 x 107 s. Find the decay rate when
3.18 x 1015 atoms are present.
Q.11 In a particular fission reaction, a 92U235 nucleus captures a slow neutron. The
fission products are 3 neutrons, a 57La142 and a fission product ZXY. What is the
value of Y and Z?
Q.12 The sequence of stepwise decay of a radioactive nucleus is
   
A ⎯⎯→ B ⎯⎯→C ⎯⎯→ D ⎯⎯→ E . If nucleon number and atomic number
for C are respectively 176 and 71, what are corresponding values for other
nuclei?
Q.13 Find the half life of a radioactive material if its activity drops to 1/16 th of its initial
value in 30 years. Also find its mean value & disintegration constant.
Q.14 The half life of a radioactive substance is 30 s. calculate the decay constant and
the time taken to decay to 3/4th of its initial value.
(0.23 /s,60s)
Q.15 A neutron is absorbed by a 3Li6 nucleus with subsequent emission of an alpha
particle. Write the nuclear reaction. Calculate the energy released in this
reaction. (Given: m(3Li6) = 6.015126 u ; m(2He4) = 4.0026044
u ; m(0n ) = 1.0086654 u ; m(1H3) = 3.016049 u )
1
238
Q.16 92U decays successively to form 90Th234 , 91Pa234 , 92U234 , 90Th230 , 88Ra226 and
222
86Rn . What are the radioactive radiations emitted in each decay?
Q.17 Two radioactive nuclei X and Y initially contain equal number of atoms. Their half
life is 1 hour and 2 hours respectively. Calculate the ratio of their rates of
disintegration after two hours.
(1:1)
Q.18 A helium nucleus of energy 10 MeV collides head on with a 29Cu64 nucleus and
retraces its path. Find the radius of Cu nucleus.
Q.19 The half life of 92U238 against alpha decay is 4.5 x 109 years. What is activity of 1g
of 92U238 ?

(1.23x104 Bq)
Q.20 Titanium has a half life of 12.5 years. What fraction of a sample of pure titanium
will remain undecayed after 25 years?
Q.21 A radioactive isotope has a half life of T years. After how much time is its activity
reduced to 6.25% of its original activity?
Q.22 Obtain the binding energy of nuclei 26Fe56 and 83Bi209 in units of MeV from the
given data: mH = 1.007825 u ; mn = 1.008665 u ; m(26Fe56) = 55.934939 u
209
; m(83Bi ) = 208.980388 u . Which nucleus has greater B.E. per nucleon?
(8.79 MeV, 7.85 MeV)
Q.23 The nucleus 10Ne23 decays by beta emission. Write the beta decay equation and
find the maximum K.E. of the electron emitted.
(Given that: m(10Ne23) = 22.994466 u ; m(11Na23) = 22.089770 u)
(4.374 MeV)
Q.24 The average energy released per fission of 94Pu239 is 180 MeV. How much
energy will release if all the atoms in 1 kg of pure 94Pu239 undergo fission?
(4.5 x 1023 MeV)
Q.25 Which one of the energy level transition will result in the emission of photon of
wavelength 620 nm? 0 eV
A - 1 eV
B D
E
- 3 eV

C
- 10 eV

Q.26 Obtain the maximum K.E. of beta particles and radiation frequencies to gamma
decays in the following decay scheme. Given that: m(198Au) = 197.968233 u and
m(198Hg) = 197.96676. 198
Au

1
1.0 8 8 MeV
2
1 3
0.412 MeV
2 0 MeV

198
Hg
Q.27 Why is the energy distribution of beta rays continuous during  - decay of a
nucleus?
Q.28 Name the reaction responsible for energy production in the sun.
Q.29 Define decay constant of a radioactive element.
Q.30 You are given 2 nuclei 3X7 and 3Y4. Which one of them is likely to be more
stable? Why?
Q.31 Draw the graph showing the variation of B.E. per nucleon with mass number of
different nuclei. State 2 inferences form the graph.
Q.32 Among ,  and  which of the radiations: (a) are similar to X – rays? (b) are
easily absorbed by matter? (c) travel with greatest speed? (d)
are similar to the cathode rays?
Q.33 Out of 14X30 , 3Y6 and 40Z130, which is more likely to undergo nuclear fission?