ATOMS — WORK BOOK/C.B.S.E.
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CH – 2 – ATOMS
Q1. The angle of scattering for zero value of impact parameter b is _________ .
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Q2. The frequency spectrum of radiation emitted as per Rutherford’s model of atom is _________ .
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Q3. The force responsible for scattering of alpha particle with target nucleus is _________ .
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Q4. According to de Broglie a stationary orbit is that which contains an _________ number of
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de Broglei waves associated with the revolting electron.
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Q5. _________ is a physical quantity whose dimensions are the same as that of Plank’s constant.
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Q6. _________ series of hydrogen spectrum lies in the visible region electromagnet spectrum.
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Q7. _________ is the ionisation potential of hydrogen atom.
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Q8. Total energy of electron in a stationary orbit is _________ which means the electron is bound
to the nucleus and is not free to leave it.
Q9. The value of Rydberg constant is _________ .
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Q10. When an electron jumbs from 2nd stationary orbit of hydrogen atom to lst stationary orbit, the
energy emitted is _________.
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Q11. The scattering angle will decrease with the _________ in mpact parameter.
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 32 —
Q12. As per Bohr model, the minimum energy (in eV) required to remove an electron from the ground
state of doubly-ionised Li atom (Z = 3) is
(a) 1.51 (b) 13.6 (c) 10.8 (d) 122.4
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Q13. The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom,
is :
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(a) 1:1 (b) 1 : –1 (c) 2 : –1 (d) 1:–2
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Q.14 The ratio of wavelengths of the last line of Balmer series and last line of Lyman series is
(a) 1 (b) 4 (c) 0.5 (d) 2
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Q15. Define the distance of closest approach. An -particle of kinetic energy ‘K’ is bombarded on a
thin gold foil. The distance of the closest approach is ‘r’. What will be the distance of closet
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approach for an -particle of double the kinetic energy ?
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 33 —
Q16. Write two important limitations of Rutherford nuclear model of the atom.
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Q17. Define ionization energy. How would the ionization energy when electrons in hydrogen atom is
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replaced by a particle of mass 200 times than that of the electron but having the same charge ?
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Q18. In an experiment on -particle scattering by a thin foil of gold, draw a plot showing the number of
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particles scattered versus the scattering angle .
Why is it that very small fraction of the particles are scattered at > 90° ?
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 34 —
Q19. Imagine removing one electron from He4 and He3. Their energy levels, as worked out on the basis
of Bohr model will be very close. Explain why.
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Q20. When an electron falls from a higher energy to a lower energy level, the difference in the energies
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appears in the form of electromagnetic radiation. Why cannot it be emitted as other forms
of energy ?
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Q21.
52 M Would the Bohr formula for the H-atom remain unchangeld if proton had a charge (+4/3)e and
electron a charge (–3/4)e, where e = 1.6 × 10–19 C ? Give reasons for your answer.
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Q22. Consider two different hydrogen atoms. The electron in each atom is in an excited state.Is it
possible for the electrons to have different energies but the same orbitl angular momentum
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according to the Bohr model ?
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Q23. The trajectories, traced by different
-particles, in Geiger-Marsden
experiment were observed as shown in
the figure.
(a) What names are given to the
symbols ‘b’ and ‘’ shown here?
(b) What can we say about the
values of b for :
(i) = 0° (ii) = radians ?
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 35 —
Q24. Suppose you are given a chance to repeat the alpha particle scattering experiment using a
thin sheet of solid hydrogen in place of gold foil (hydrogen is a solid at temperature below 14K.
What result do you expect ?
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Q25.
52 M Determine the distance of closest approach when an alpha particle of kinetic energy 4.5 MeV
strikes a nucleus of Z = 80, stops and reverses its direction.
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Q26. A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation
emitted when the atom makes transition from the upper level to the lower level ?
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 36 —
Q27. The ground state energy of hydrogen atom is –13.6 eV. What is the kinetic and potential energies
of the electron in this state ?
OR
Given the value of the ground state energy of hydrogen atom is –13.6 eV, find out its kinetic and
potential energy in the ground and second excited states ?
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Q28. Using de Broglie’s hypothesis, explain with the help of a suitable diagram, Bohr’s second postulate
of quantisation of energy levels in a hydrogen atom.
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 37 —
Q29. A hydrogen atom initially in the ground state absorbs a photon, which excites it to the n = 4 level.
Detetermine the wavelength and frequency of photon.
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Q30. (a) Using the Bohr’s model, calculate the speed of electron in the hydrogen in n = 1, 2 and
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3 levels.
(b) Calculate the orbital period in each of these levels.
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 38 —
Q31. What is the longest wavelength photon that can ionize a hydrogen atom in its ground state ?
Specify the type of radiation.
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Q32. In Bohr’s theory of hydrogen atom, calculate the energy of the photon emitted during a transition
of the electron from the first excited state to the ground state. Write in which region of the electro
magnetic spectrum this transition lies.
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Q33. The energy level diagram of an element is given below. Identify, by doing necessary calculations,
which transition corresponds to the emission of a spectral line of wavelength 102.7 nm.
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Q34. The energy levels of an atom are given below in the diagram.
Which of the transitions belong to Lyman and Balmer series ? Calculate the ratio of the shortest
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wavelengths of the Lyman and Balmer series of the the spectra.
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Q35. A radioactive isotope has a half-life of 5 years. After how much time is its activity reduced to
3.125% of its origonal activity.
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Q36. When four hydrogen nuclei combine to form a helium nucleus, estimate the amount of energy in
MeV released in the proces of fusion. (Neglect the masses of electron and neutrons). Given :
(i) mass of 11 H = 1.007825u
(ii) mass of helium nucleus = 4.002603u, 1u = 931 MeV/c2.
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 40 —
Q37. 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 ?
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Q38. Draw a schematic arrangement of Geiger-Marsden experiment for studying -particle scattering
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by a thin foil of gold. Describe briefly, by drawing trajectories of the scattered -particles. How
this study can be used to estimate the size of the nucleus ?
OR
Describe Geiger-Marsden experiment. What are its observations and conclusions ?
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Q39. The spectrum of a star in the visible and the ultraviolet region was observed and the wavelength of
some of the lines that could be identified were found to be :
824Å, 970Å, 1120Å, 2504Å, 5173Å, 6100Å
Which of these lines cannot belong to hydrogen atom spectrum ?
1
(Given Rydberg constant R 1.03 107 m 1 and 970Å . Support your answer with
R
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suitable calculation.
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Q40. Rutherford’s atomic model was a reasonably good model of structure of atom based on the
famous a particle scattering experiment. However, it was subsequently modified by Neils Bohr
and later on, by others. The resulting improvements in the understanding of atomic structure have
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greatly contributed to further scientific advancement. There are many other similar examples in
scientific field when original contributors happily accept modifications in their ideas.
Answer the following questions based on the above information :
(i) Write two major drawbacks of Rutherford’s atomic model. How were these drawbacks
overcome in Neils Bohr Model ?
(ii) Name two scientific values associated with the above anecdote.
(iii) How are these values helpful to an individual in daily ilfe ?
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 42 —
Q41. A photon emitted during the de-excitation of electron from a state n to the first excited state in
a hydrogen atom, irradiates a metallic cathode of work function 2eV, in a photo cell, with a
stopping potential of 0.55V. Obtain the value of the quantum number of the state n.
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Q42. (a) State Bohr’s quantization condition for defining stationary orbits. How does de Broglie
hypothesis explain the stationary orbits ?
(b) Find the relation between the three wavelengths 1, 2 and 3 from the energy level
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 43 —
Q43. An electron jumps from fourth to first orbit in an atom. How many maximum number of spectral
lines can be emitted by the atom ? To which series these lines correspond ?
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Q44. The energy levels of an atom of element X are shown in the diagram. Which one of the level
transitions will result in the emission of photons of wavelength 620 nm ? Support your answer with
mathematical calculations.
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 44 —
Q45. (a) State Bohr’s postulate to define stable orbits in hydrogen atom. How does de Broglie’s
hypothesis explain the stability of these orbits ?
(b) A hydrogen atom initially in the ground state absorbs a photon which excites it to the
a = 4 level. Estimate the frequency of the photon.
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 45 —
Q46. The ground state energy of hydrogen atom is –13.6 eV. If an electron makes a transition from an
energy level –1.51 eV to – 3.4 eV, calculate the wavelength of the spectral line emitted and name
the series of hydrogen spectrum to which it belongs.
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Q47. A hydrogen atom initially in its ground state absorbs a photon and is in the excited state with energy
12.5 eV. Calculate the longest wavelength of the radiation emitted and identify the series to which
it belongs. [Take Rydberg constant R = 1.1 × 107 m–1]
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Q48. Obtain the first Bohr’s radius and the ground state energy of a muonic hydrogen atom, i.e., an
atom where the electron is replaced by a negatively charged muon (–) of mass about 207m, that
orbits around a proton.
(Given for hydrogen atom, radius of first orbit and ground state energy are 0.53 × 10–10 m and
–13.6 eV respectively).
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 46 —
Q49. The short wavelength limit for the Lymen series of the hydrogen spectrum is 913.4Å. Calculate the
short wavelength limit for Balmer series of the hydrogen spectrum.
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Q50. Derive the expression for the magnetic field at the site of a point nucleus in a hydrogen atom due
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to the circular motion of the electron. Assume that the atom is in its ground state and give the
answer in terms of fundamental constants.
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 47 —
Q51. Show that the radius of the orbit in hydrogen atom varies as n2, where n is the principal quantum
number of the atom.
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Q52.
52 M State Bohr’s postulate of hydrogen atom which successfully explains the emission lines in the
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spectrum of hydrogen atom. Use Rydberg formula to determine the wavelength of H line.
[Given Rydberg constant R = 1.03 × 107 m–1]
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Q53. Using Rydberg’s formula, calculate the longest wavelengths belonging to Lyman and Balmer
series. In which region of hydrogen spectrum do these transition lie ? [Given R = 1.1 × 107 m–1]
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Q54. Using Rutherford model of the atom, derive the expression for the total energy of the electron
in hydrogen atom. What is the significance of total negative energy possessed by the electron ?
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Q55. Using Bohr’s postulates of the atomic model, derive the expression for radius of nth electron orbit.
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Hence, obtain the expression for Bohr’s radius.
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Q56. 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 member
of Lyman and the first member of Balmer series.
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Q57. A 12.9 eV beam of electrons is used to bombard gaseous hydrgen at room temperature. Upto
which energy level the hydrogen atoms would be excited ? Calculate the wavelength of the first
member of Paschen series and first member of Balmer series.
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 50 —
Q58. Using Bohr’s postulates, obtain the expressions 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 transition between energy levels result in the appearance of Lyman series.
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 51 —
Q59. (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.
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(b) Which of these transitions corresponds to the emission of radiation of :
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(i) maximum and (ii) minimum wavelength ?
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 52 —
Q60. (a) 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.
(b) 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 ?
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 53 —
Q61. 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 wavelenglth of the spectral line emitted. To
which series of hydrogen spectrum does this wavelength belong ?
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Q62.
52 M Using the postulate of Bohr’s model of hydrogen atom, obtain an expression for the frequency of
radiation emitted when the atom makes a transition from the higher energy state with quantum
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number n i to the lower energy state with quantum number n f (n f n i ).
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Q63. What is the ratio of radii of the orbits corresponding to first excited state and ground state in
a hydrogen atom ?
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Q64. The radius of innermost electron orbit of a hydrogen atom is 5.3 1011 m. What is the radius of
orbit in the second excited state ?
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Q65. Write the expression for Bohr’s radius in hydrogen atom.
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Q66. Define ionisation energy. What is its value for a hydrogen atom ?
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Q67. Find the ratio of energies of photon produced due to transition of an electron of hydrogen atom
from its :
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(i) second permitted energy level to the first level, and
(ii) the highest permitted energy level to the first permitted level.
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Q68. The ground state energy of hydrogen atom is – 13.6 eV. What are the kinetic and potential
energies of electron in this state ?
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Q69. State Bohr’s quantisation condition for defining stationary orbits.
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Q70. In the Rutherford scattering experiment the distance of closest approach for an -particle is d 0 .
If -particle is replaced by a proton, how much kinetic energy in comparison to -particle will it
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require to have the same distance of closest approach d0 ?
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Q71. In the study of Geiger-Marsden experiment on scattering of — particles by a thin foil of gold,
draw the trajectory of — particles in the coulomb field of target nucleus. Explain briefly how
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one gets the information on the size of the nucleus from this study.
From the relation R R 0 A1/3 , where R is constant and A is the mass number of the nucleus,
0
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show that nuclear matter density is independent of A.
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Q72. In a Geiger – Marsden experiment,calculate the distance of closest approachto 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 approachbe affected when the kinetic energy of the — particle
is doubled ?
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ATOMS — WORK BOOK/C.B.S.E./PHYSICS XII — 58 —
Q73. Draw a schematic arrangement of the Geiger—Marsden experiment. How did the scattering of
— particle by a thin foil of gold provide an important way to determine an upper limit on the size
of the nucleus ? Explain briefly ?
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