ASSIGNMENT PHYSICS : ATOMS & NUCLEI

SANCHAY COACHING CENTRE
SCO 99, Sector 10A, Gurgaon
9810710607, 9871471473
Atoms & Nuclei—XII

1. A nucleus 23 Ne 10 undergoes β – decay and becomes 23 Na 11 . Calculate the maximum kinetic energy of electrons
emitted assuming that the daughter nucleus and anti-neutrino carry negligible kinetic energy.
3. Name the absorbing material used to control the reaction rate of neutrons in a nuclear reactor.
4. State two characteristics properties of nuclear force.
6. The ground state energy of hydrogen atom is – 13.6 eV. (i) What is the kinetic energy of the electron in the 2 nd
excited state (ii) If the electron jumps to the ground state from the 2 nd excited state, calculate the wavelength of the
spectral line emitted.
7. Two nuclei have mass numbers in the ratio 1:2. What is the ratio of their nuclear densities?

9. Two nuclei have mass numbers in the ration 1:8. What is the ratio of their nuclear radii?
10. (a) The mass of a nucleus in its ground state is always less than the total mass of its constituents – neutrons and
protons. Explain.
(b) Plot a graph showing the variation of potential energy of a pair of nucleons as a function of their separation.
11. Draw a plot showing the variation of binding energy per nucleon versus the mass number A. Explain with the help of
this plot the release of energy in the processes of nuclear fission and fusion.
12. Define the activity of a radionuclide. Write its SI unit. Give a plot of the activity of a radioactive species versus time.
How long will a radioactive isotope, whose half-life is T years, take for its activity reduce to 1/8 th of its initial value?
13. What is the ratio of radii of the orbits corresponding to first excited state and ground state in a hydrogen atom?
14. A heavy nucleus X of mass number 240 and binding energy per nucleon 7.6 MeV is split into two fragments Y and Z
of mass numbers 110 and 130. The binding energy of nucleons in Y and Z is 8.5 MeV per nucleon. Calculate the
energy released Q per fission in MeV.
16. Write the expression for Bohr’s radius in Hydrogen atom.
17. Define ionisation energy. What is its value for a Hydrogen atom?
18. Deduce the expression for the magnetic dipole moment of an electron orbiting around the central nucleus.
19. Draw a plot of potential energy of a pair of nucleons as a function of their separation. Write two important
conclusions which you can draw regarding the nature of nuclear forces.
20. How will you explain the constancy of binding energy per nucleon in the range 30 < A < 170 using the property that
nuclear force is short ranged?
21. Write symbolically the β – decay process of 32 P 15 . Derive an expression for the average life of a radionuclide. Give its
relationship with the half-life.
22. Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second
permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.
23. The ground state energy of hydrogen atom is -13.6 eV. What are the kinetic and potential energies of electron in
this state?
25. Using de-Broglie’s hypothesis, explain with the help of suitable diagram, Bohr’s second postulate of quantization of
energy levels in the hydrogen atom.
26. Show that the density of nucleus over a wide range of nuclei is constant – independent of mass number A.
27. Draw a plot of potential energy of a pair of nucleons as a function of their separations. Mark the regions where the
nuclear force is (i) attractive (ii) repulsive.
28. In a Geiger-Marsden experiment, calculate the distance of closest approach to the nucleus of Z = 80, when an
alpha particle of 8 MeV energy impinges on it before it comes momentarily to rest and reverses its direction. How
will the distance of closest approach be affected when the kinetic energy of the alpha particle is doubled?

29. The ground state energy of the hydrogen atom is -13.6 eV. If an electron makes a transition from an energy level –
0.85 eV to -3.4 eV, calculate the wavelength of the spectral line emitted. To which series of hydrogen spectrum
does this wavelength belong?
30. Why is the classical (Rutherford) model for an atom – of electron orbiting around the nucleus – not able to explain
the atomic structure?
31. (a) Using Bohr’s theory of hydrogen atom, derive the expression for the total energy of the electron in the stationary
states of the atom.
(b) If electron in the atom is replaced by a particle (muon) having the same charge but mass about 200 times as
that of the electron to form a muonic atom, how would (i) the radius and (ii) the ground state energy of this be
affected?
(c) Calculate the wavelength of the first spectral line in the corresponding Lyman series of this atom.
32. A radioactive isotope has a half-life of T years. How long will it take the activity to reduce to 3.125 % of its original
value? When a nucleus (X) undergoes beta decay, and transforms to the nucleus (Y), does the pair (X,Y) form
isotopes, isobars or isotones? Justify your answer.
33. What is the relationship between the half-life and mean life of a radioactive nucleus?
34. (i) In hydrogen atom, an electron undergoes transition from 2 nd excited state to the first excited state. Identify the
spectral series to which this transitions belong.
(ii) Find out the ratio of the wavelengths of the emitted radiations in the two cases.
35. Answer the following: (i) When a heavy nucleus with mass number A = 240 breaks into two nuclei, A = 120, energy
is released in the process. (ii) In beta decay, the experimental detection of neutrinos or antineutrinos is found to be
extremely difficult.
36. What is the relationship between the size and the atomic mass number of a nucleus?
38. Using Bohr’s postulates, obtain the expression for the total energy of the electron in the stationary states of the
hydrogen atom. Hence draw the energy level diagram showing how the line spectra corresponding to Balmer series
occur due to transition between energy levels.
39. Using Bohr’s postulates, obtain the expressions for (i) KE and (ii) PE, of the electron in stationary state of hydrogen
atom. Draw the energy level diagram showing how the transitions between energy levels result in the appearance of
Lyman series.
40. When is H α line of the Balmer series in the emission spectrum of hydrogen atom is obtained?
41. In the ground state of hydrogen atom, its Bohr radius is given as 5.3X10 -11 m. The atom is excited such that the
radius becomes 21.2X10 -11 m. Find (i) the value of the principle quantum number and (ii) the total energy of the
atom in this excited state.
43. What is the maximum number of spectral lines emitted by a hydrogen atom when it is in the 3 rd excited state?
44. Show that the electron revolving around the nucleus in a radius r with orbital speed v has magnetic moment evr/2.
Hence using Bohr’s postulates of the quantisation of angular momentum, obtain the expression for the magnetic
moment of hydrogen atom in its ground state.
45. A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. Upto which energy level the
hydrogen atoms would be excited? Calculate the wavelengths of the first members of Lyman and the first member
of Balmer series.
47. Why is it found experimentally difficult to detect neutrinos in nuclear β-decay?
48. Using Rutherford model of the atom, derive the expression for the total energy of the electron in the hydrogen atom.
What is the significance of total negative energy possessed by the electron?
49. The radius of the innermost electron orbit of a hydrogen atom is 5.3 X 10 -11 m. Calculate its radius in n = 3 orbit.
50. The value of ground state energy of hydrogen atom is 13.6 eV. (i) find the energy required to move an electron from
the ground state to the first excited state of the atom.(ii) Determine the KE and the orbital radius in the first excited
state of the atom. (Given the value of Bohr radius = 0.53 Å.
51. The half-life of 238 U 92 undergoing α – decay is 4.5 X 10 9 years. Determine the activity of 10g sample of U-238. Given
that 1 g of U-238 contains 25.3 X 10 20 atoms.
52. (i) Define the term ‘mass defect’ of a nucleus. How is it related with the binding energy?
(ii) Determine the Q-value of the following reaction: 1 H 1 + 3 H 1 2 H 1 + 2 H 1 , given masses are 2 H 1 = 2.014102 u,
3 H 1 = 3.016049u , 1 H 1 = 1.00783 u.
53. A hydrogen atom initially in the ground state absorbs a photon which excites it to n = 4 level. Determine the
wavelength of this photon.
54. Show that the radius of the orbit in hydrogen varies as n 2 , where n is the principal quantum number of the atom.
55. In the study of Geiger – Marsden experiment on scattering of alpha particles by a thin foil of gold, draw the
trajectory of α-particles in the coulomb field of target nucleus. Explain briefly how one gets the information on the
size of the nucleus from this study.
56. Distinguish between nuclear fission and fusion. Show how in both these processes energy is released.