ATOMS AND NUCLEI
MARK QUESTIONS
1. What is the ratio of radii of the orbits corresponding to first excited state and ground state in a hydrogen
atom?
[CBSE DELHI 2010]
2. The radius of innermost electron orbit of a hydrogen atom is 53×10-11m. What is the radius of orbit in the
second excited state?
[CBSE DELHI 2010]
3. Write the expression for Bohr’s radius in hydrogen atom.
[CBSE DELHI 2010]
4. Define ionization energy. What is its value for a hydrogen atom?
[CBSE ALL INDIA 2010]
5. 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.
[CBSE ALL INDIA 2010]
6. The ground state energy of hydrogen atom is – 13.6 eV. What are the kinetic and potential energies of
electron in this state?
[CBSE ALL INDIA 2010]
7. State Bohr’s quantization condition for defining stationary orbits.
[CBSE FOREIGN 2010]
8. Show graphically, the variation of the de-Broglie wavelength ( ) with the potential (V) through which an
electron is accelerated from rest.
[CBSE DELHI 2011]
9. Write any two characteristic properties of nuclear force.
[CBSE ALL INDIA 2011]
10. Define the term ‘threshold frequency’ in relations to photoelectric effects.
[CBSE FOREIGN 2011]
11. Show the variation of photocurrent with collector plate potential for different frequencies but same
intensity of incident radiation.
[CBSE FOREIGN 2011]
12. Name the physical quantity which remains same for microwaves of wavelength 1 mm and UV radiations
of 1600 Å in vacuum.
[CBSE DELHI 2012]
13. State de-Broglie hypothesis.
[CBSE DELHI 2012]
14. A proton and an electron have same kinetic energy. Which one has greater de-Broglie wavelength and
why?
[CBSE ALL INDIA 2012]
15.
square root of accelerating potential(V).
[CBSE FOREIGN 2012]
16. Show on a graph variation of the deV,
where V is the accelerating potential for the electron.
[CBSE FOREIGN 2012]
17. Write the relation between de-Broglie wavelength λ associated with the electron and its kinetic energy E.
[CBSE FOREIGN 2012]
18. The given graph shows the variation of photo-electric current (I) versus applied voltage (V) for two
different photosensitive materials and for two different intensities of the incident radiation. Identify the
pairs of curves that correspond to different materials but same intensity radiation.
[CBSE DELHI 2013]
19. Write the expression for the de Broglie wavelength associated with a charged particle having charge ‘q’
and mass ‘m’, when it is accelerated by a potential V.
[CBSE ALL INDIA 2013]
2 MARK QUESTIONS
1. An electron is accelerated through a potential difference of 100 volts. What is the de-Brogliewavelength
associated with it? To which part of the electromagnetic spectrum does this value ofwavelength
correspond?
[CBSE DELHI 2010]
2. A heavy nucleus X of mass number 240 and binding energy per nucleon 7.6 MeV is split into
twofragments Y and Z of mass numbers 110 and 130. The binding energy of nucleons in Y and Z is8.5 MeV
per nucleon. Calculate the energy Q released per fission in MeV.
[CBSE DELHI 2010]
3. An electron is accelerated through a potential difference of 144 volts. What is the de-Broglie wavelength
associated with it? To which part of the electromagnetic spectrum does this wavelength correspond?
[CBSE DELHI 2010]
4. An electron is accelerated through a potential difference of 64 volts. What is the de-Broglie wavelength
associated with it? To which part of the electromagnetic spectrum does this value of wavelength
correspond?
[CBSE DELHI 2010]
5. A α-particle and a proton are accelerated from rest by the same potential. Find the ratio of their deBroglie wavelengths.
[CBSE ALL INDIA 2010]
6. Write Einstein’s photoelectric equation. State clearly the three salient features observed in photoelectric
effect, which can be explained on the basis of the above equation.
[CBSE ALL INDIA 2010]
7. 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.
OR
Draw a plot of the binding energy per nucleon as a function of mass number for a large number of nuclei,
2 <=A<= 240. How do you explain the constancy of binding energy per nucleon in the range 30< A<170
using the property that nuclear force is short-ranged? Nuclear forces are short ranged, so every nucleon
interacts with their neighbors only; so binding energy per nucleon remains constant.
[CBSE ALL INDIA 2010]
8. If both the number of protons and the number of neutrons are conserved in a nuclear reaction like
in what way is mass converted into energy? Explain.
[CBSE FOREIGN 2010]
9. When four hydrogen nuclei combine to form a helium nucleus, estimate the amount of energy in MeV
released in this process of fusion (Neglect the masses of electrons and neutrinos) Given:
(a) mass of
= 1.007825 u
(b) mass of helium nucleus = 4.002603 u, 1u = 931 MeV/ c2
[CBSE FOREIGN 2011]
10. Ultraviolet light of wavelength 2271 A from 100 W mercury source irradiates a photocell made of
molybdenum metal. If the stopping potential is –1.3 V, estimate the work function of the metal. How
would the photocell respond when the source is replaced by another source of high intensity (~10^5
o
Wm^. Justify your answer.
[CBSE FOREIGN 2013]
o
11. An electron and a proton, each have de Broglie wavelength of 1.00 nm.
(a) Find the ratio of their momenta.
(b) Compare the kinetic energy of the proton with that of the electron.
[CBSE FOREIGN 2013]
12. A proton and an alpha particle are accelerated through the same potential. Which one of the two has (i)
greater value of de-Broglie wavelength associated with it and (ii) less kinetic energy. Give reasons to
justify your answer.
[CBSE ALL INDIA 2014]
13. A proton and an α-particle have the same de-Broglie wavelength. Determine the ratio of (i) their
accelerating potentials (b) their speeds.
[CBSE ALL INDIA 2015]
14. Show that the radius of the orbit in hydrogen atom varies as n2, where n is the principal quantum number
of atom.
[CBSE ALL INDIA 2015]
3 MARK QUESTIONS
1. (i) Define ‘activity’ of a radioactive material and write its S.I. unit.
(ii) Plot a graph showing variation of activity of a given radioactive sample with time.
(iii) The sequence of stepwise decay of a radioactive nucleus is
2. If the atomic number and mass number of D2 are 71 and 176 respectively, what are their
corresponding values for D ?
[CBSE DELHI 2010]
4. Write symbolically the α-decay process of
Derive an expression for the average life of a radionuclide. Give its relationship with the half-life.
[CBSE ALL INDIA 2010]
5. Draw a schematic arrangement of the Geiger – Marsden experiment for studying α-particle scattering by
a thin foil of gold. Describe briefly, by drawing trajectories of the scattered α-particle, how this study can
be used to estimate the size of the nucleus.
[CBSE FOREIGN 2010]
6. An electron and a photon each have a wavelength 1.00 nm. Find (a) .their momenta, (b)the energy of the
photon and (c) the kinetic energy of electron
[CBSE DELHI 2011]
7. The energy levels of a hypothetical atom are shown below. Which of the shown transitions will result in the
emission of a photon of wavelength 275 nm? Which of these transitions correspond to emission of
radiation of (i) maximum and (ii) minimum wavelength?
[CBSE DELHI 2011]
8. An electron and a photon each have a wave length of 1.50 nm. Find (i) their momenta, (ii) the energy of
the photon and
(iii) Kinetic energy of the electron.
[CBSE DELHI 2011]
9. An electron and a photon each have a wavelength of 2 nm. Find
a. their momenta
b. the energy of the photon
c. the kinetic energy of the electron.
[CBSE DELHI 2011]
9. Draw a plot showing the variation of photoelectric current with collector plate potential for two different
frequencies, v1 and v2 , of incident radiation having the same intensity. In which case will the stopping
potential be higher? Justify your answer.
[CBSE ALL INDIA 2011]
10. Using de Broglie’s hypothesis, explain with the help of a suitable diagram, Bohr’s second postulate of
quantization of energy levels in a Hydrogen atom. The ground state energy of hydrogen atom is –13.6
eV. What are the kinetic and potential energies of the electron in this state?
[CBSE ALL INDIA 2011]
11. Using the postulates of Bohr's model of hydrogen atom, obtain an expression for the frequency of
radiation emitted when atom make a transition from the higher energy state with quantum number ito
the lower energy state with quantum number nf (nf˃ni).
[CBSE FOREIGN 2011]
12. Using Bohr’s second postulate of quantization of orbital angular momentum show that the
circumference of the electron in the nth orbital state in hydrogen atom is n times the de Broglie
wavelength associated with it.
13. The electron in hydrogen atom is initially in the third excited state. What is the maximum number of
spectral lines which can be emitted when it finally moves to the ground state? [CBSE DELHI 2012]
14. (i) What characteristic property of nuclear force explains the constancy of binding energy per nucleon
(BE/A) in the range of mass number ‘A’ lying 30 <A < 170?
(ii) Show that the density of nucleus over a wide range of nuclei is constant independent of mass
number A.
[CBSE DELHI 2012]
15. Write Einstein’s photoelectric equation. State clearly how this equation is obtained using the photon
picture of electromagnetic radiation. Write the three salient features observed in photoelectric effect
which can be explained using this equation.
[CBSE DELHI 2012]
16. Define the terms (i) ‘cut-off voltage’ and (ii) ‘threshold frequency’ in relation to the phenomenon of
photoelectric effect.
17. Using Einstein’s photoelectric equation show how the cut-off voltage and threshold frequency fora given
photosensitive material can be determined with the help of a suitable plot/graph.
[CBSE ALL INDIA 2012]
18. 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 and (ii) repulsive. Write any two characteristic features of nuclear
forces.
[CBSE ALL INDIA 2012]
19. In a Geiger–Marsden experiment, calculate the distance of closest approach to the nucleus of Z =80,
when an -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 α- particle
is doubled?
20. The ground state energy of 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?
[CBSE ALL INDIA 2012]
21. In a Geiger– Marsden experiment, calculate the distance of closest approach to the nucleus of Z
-particle of 5 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 α particle is doubled?
22. The ground state energy of hydrogen atom is –13.6 eV. If an electron makes a transition from an energy
level – 0.85 eV to – 1.51 eV, calculate the wavelength of the spectral line emitted. To which series of
hydrogen spectrum does this wavelength belong?
[CBSE ALL INDIA 2012]
23. Write two characteristic features observed in photoelectric effect which support the photon picture of
electromagnetic radiation.
24. Draw a graph between the frequency of incident radiation (v) and the maximum kinetic energy of the
electrons emitted from the surface of a photosensitive material. State clearly how this graph can be used
to determine (i) Planck’s constant and (ii) work function of the material.
[CBSE FOREIGN 2012]
25. Using Bohr’s postulates for hydrogen atom, show that the total energy (E) of the electron in the
stationary states can be expressed as the sum of kinetic energy (K) and potential energy (U), where K = –
2U. Hence deduce the expression for the total energy in the nth energy level of hydrogen atom.
[CBSE FOREIGN 2012]
26. (a) In a typical nuclear reaction, e.g.
although number of nucleons is conserved, yet energy is released. How? Explain.
(b) Show that nuclear density in a given nucleus is independent of mass number A.
[CBSE DELHI 2013]
27. (a) Why photoelectric effect cannot be explained on the basis of wave nature of light? Give reasons. (b)
Write the basic features of photon picture of electromagnetic radiation on which Einstein’s photoelectric
equation is based.
[CBSE DELHI 2013]
28. 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. [CBSE DELHI 2013]
29. Using Bohr’s postulates, obtain the expression for (i) kinetic energy and (ii) potential energy 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 Lymann Series. [CBSE DELHI 2013]
30. (a) In a nuclear reaction
31.
32.
33.
34.
35.
though the number of nucleons is conserved on both sides of the
reaction, yet the energy is
released. How? Explain.
(b) Draw a plot of potential energy between a pair of nucleons as a function of their separation.
Mark
The regions where potential energy is (i) positive and (ii) negative.
[CBSE DELHI 2013]
(a) Using Bohr’s postulates, obtain the expression for total energy of the electron in the nth orbit of
hydrogen atom.
(b) What is the significance of negative sign in the expression for the energy?
(c) Draw the energy level diagram showing how the line spectra corresponding to Paschen series occur
due to transition between energy levels.
[CBSE DELHI 2013]
Write Einstein’s photoelectric equation and point out any two characteristic properties of photons on
which this equation is based.
Briefly explain the three observed features which can be explained by this equation.
[CBSE ALL INDIA 2013]
In an experiment on α-particle scattering by a thin foil of gold, draw a plot showing the number of
particles scattered versus the scattering angle θ. Why is it that a very small fraction of the particles are
scattered at θ? Write two important conclusions that can be drawn regarding the structure of the atom
from the study of this experiment.
36. Derive the expression for the law of radioactive decay of a given sample having initially N0 nuclei
decaying to the number N present at any subsequent time t. Plot a graph showing the variation of the
number of nuclei versus the time t lapsed. Mark a point on the plot in terms of T1/2 value when the
number present N = N0 /16.
[CBSE FOREIGN 2013]
37.
(a) The energy levels of a hypothetical hydrogen-like atom are shown in the figure. Find out the
transition, from the ones shown in the figure, which will result in the emission of a photon of
wavelength 275 nm.
(b) Which of these transitions corresponds to the emission of radiation of (i) maximum and (ii) minimum
wavelength?
[CBSE FOREIGN 2013]
38. A proton and an alpha particle are accelerated through the same potential. Which one of the two has(i)
greater value of de-Broglie wavelength associated with it and (ii) less kinetic energy. Give reasons to
justify your answer.
[CBSE ALL INDIA 2014]
39. Write Einstein’s photoelectric equation and mention which important features in photoelectric effect
can be explained with the help of this equation. The maximum kinetic energy of the photoelectrons gets
doubled when the wavelength of light incident on the surface changes from
. Derive the
expressions for the threshold wavelength
and work function for the metal surface.
[CBSE ALL INDIA 2015]
40. Distinguish between nuclear fission and fusion. Show how in both these processes energy is released.
Calculate the energy release in MeV in the deuterium-tritium fusion reaction:
[CBSE ALL INDIA 2015]
5 MARK QUESTIONS
1. Using Bohr’s postulates, derive the expression for the frequency of radiation emitted when electron in
hydrogen atom undergoes transition from higher energy state (quantum number ni) to the lower state, (nf).
When electron in hydrogen atom jumps from energy state n= 4 to n= 3, 2,1, identify the spectral series to
which the emission lines belong.
Or
(a) Draw the plot of binding energy per nucleon (BE/A) as a function of mass number A. Write two important
conclusions that can be drawn regarding the nature of nuclear force.
(b) Use this graph to explain the release of energy in both the processes of nuclear fusion and fission.
(c) Write the basic nuclear process of neutron undergoing B–decay. Why is the detection of neutrinos found
very difficult?
[CBSE ALL INDIA 2013]