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Choose the correct alternative from clues given at end of the each statement:
(a) The size of the atom in Thomson's model is ...... the atomic size in Rutherford's model.
(much greater than/no different from/much less than.)
(b) In the ground state of ...... electrons are in stable equilibrium, while in...... electrons always experience a net force.
(Thomson's model/Rutherford's model.)
(c) A classical atom based on ...... is doomed to collapse.
(Thomson's model/Rutherford's model.)
(d) An atom has a nearly continuous mass distribution in a ...... but has a highly non-uniform mass distribution in .......
(Thomson's model/Rutherford's model.)
(e) The positively charged part of the atom possesses most of the mass in (Rutherford's model/both the models.)
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Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperature 14 K). What results do you expect ?
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What is the shortest wavelength present in the Paschen series of spectral lines ?
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A difference of 233 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom transits from the upper level to the lower level ?
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The ground state energy of hydrogen atom is -13.6 eV. What are the kinetic and potential energies of the electron in this state ?
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A hydrogen atom initially in the ground level absorbs a photon which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
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(a) Using the Bohr's model, calculate the speed of the electron in a hydrogen atom in the n = 1, 2 and 3 levels, (b) Calculate the orbital period in each of these levels.
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The radius of the
innermost electron orbit of a hydrogen atom is
. What are
the radii of the w = 2 and n = 3 orbits ?
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A 12-5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted ?
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In accordance
with the Bohr's model, find the quantum number that characterises the earth's
revolution around the sun in an orbit of radius 1-5 x 1011 m with
orbital speed
(Mass of earth = 6-0 x
1024 kg.)
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Answer the following questions, which help you understand
the difference between Thomson's model and Rutherford's model better.
(a) Is the average angle of deflection of 
particles by a thin gold foil predicted by Thomson's model
much less, about the same, or much greater than that predicted by Rutherford's
model ?
(b) Is the
probability of backward scattering (i.e., scattering of particles at angles greater than 90°) predicted by Thomson's
model much less, about the same, or much greater than that predicted by
Rutherford's model ?
(c) Keeping other factors fixed, it is found experimentally
that for small thickness t, the number of a-particles scattered at moderate
angles is proportional to t.
What clue does this linear independence on t provide ?
(d) In which model
is it completely wrong to ignore multiple scattering for the calculation of
average angle of scattering of a-particles by a thin foil ?
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The gravitational
attraction between electron and proton in a hydrogen atom is weaker than the
coulomb attraction by a factor of about
. An alternative way
of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen
atom if the electron and proton were bound by gravitational attraction.
You will find,
the answer interesting.
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Obtain an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level n to level (n -1). For large n, show that this frequency equals the classical frequency of revolution of the electron in the orbit.
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Classically, an
electron can be in any orbit around the nucleus of an atom.
Then what
determines the typical atomic size ? Why is an atom not, say, thousand times
bigger than its typical size ? The question had greatly puzzled Bohr before he
arrived at his famous model of the atom that you have learnt in the text. To stimulate
what he might well have done before his discovery, let us play as follows with
the basic constants of nature and see if we can get a quantity with the dimensions
of length that is roughly equal to the known size of an atom
(a) Construct
a quantity with the dimensions of length from the fundamental constants c,
and
c. Determine its numerical value.
(b)
You will find that the length obtained in (a) many orders of magnitude smaller than
the atomic dimensions. Further, it involves c. But energies of atoms are mostly
in non-relativistic domain where c is not expected to play any role. This is what
may have suggested Bohr to discard c and look for 'something else' to get the right
atomic size. Now, the Planck's constant h had already made its appearance
elsewhere. Bohr's great
insight lay in
recognising that A,
and e will yield the
right atomic size. Construct a quantity with the dimension of length from h, m^
and e and confirm that its numerical value has indeed the correct order of
magnitude.
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The total energy of an electron in the first excited state of the hydrogen atom is about - 3.4 eV.
(a) What is the kinetic energy of the electron in this state ?
(b) What is the potential energy of the electron in this state ?
(c) Which of the answers above would change if the choice of the zero of potential energy is changed ?
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If Bohr's
quantisation postulate (angular momentum
) is a basic
law of nature, it should be equally valid for the case of planetary motion
also. Why then do we never speak of quantisation of orbits of planets around
the sun ?
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question_answer17)
Taking the Bohr
radius as A0 = 53 pm, the radius of 
ion
in its ground state, on the basis of Bohr's model, will be about
(a)
53pm (b) 27 pm
(c)
18 pm (a) 13 pm
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question_answer18)
The binding energy
of a H-atom, considering an electron moving around a fixed nuclei (proton), is 
(m = electron mass).
If one
decides to work in a frame of reference where the electron is at rest, the
proton would be moving around it By similar arguments, the binding energy
would be
This
last expression is not correct because
(a) n would not be integral
(b )Bohr-quantisation applies only to electron
(c) the frame in which the electron is at rest is not
inertial
(d) the motion of the proton would not be in circlar
orbits, even approximately
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question_answer19)
The simple Bohr
model can not be directly applied to calculate the energy levels of an atom
with many electrons. This is because
(a) of the electrons not being subject to a central force
(b) of the
electrons colliding with each other
(c) of
screening effects
(d) the force between the nucleus and an electron will no
longer be given by Coulomb's law
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question_answer20)
For the ground
state, the electron in the H- atom has an angular momentum = h, according to
the simple Bohr model. Angular momentum is a vector and hence there
will be infinitely many orbits with the vector pointing in all
possible directions. In actuality, this is not true.
(a) because Bohr model gives incorrect values of angular
momentum
(b) because
only one of these would have a minimum energy
(c) angular
momentum must be in the direction of spin of electron
(d) because electrons go around only in horizontal orbits
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question_answer21)
molecule consists of two oxygen
atoms. In the molecule, nuclear force between the nuclei of the two
atoms
(a) is not important because nuclear forces are short-ranged
(b) is as
important as electrostatic force for binding the two atoms
(c) cancels
the repulsive electrostatic force between the nuclei
(d) is not important because oxygen nucleus have equal
number of neutrons and protons
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question_answer22)
Two H atoms in the
ground state collide inelastically. The maximum amount by which their combined
kinetic energy is reduced is
(a) 
(b) 
(c)
(a)
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question_answer23)
A set of atoms in
an excited state decays.
(a) in general to any of the states with lower energy
(b) into a
lower state only when excited by an external electric field
(c) all
together simultaneously into a lower state
(d) to emit photons only when they collide
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question_answer24)
An ionised
H-molecule consists of an electron and two protons. The protons are separated by
a small distance of the order of angstrom. In the ground state,
(a) the electron would not move in circular orbits
(b)the energy would be (2)4 times that of a H-
atom
(c) the
electrons, orbit would go arround the protons
(d)
the molecule will soon decay in a proton and a H-atom
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question_answer25)
Consider aiming a
beam of free electrons towards free protons. When they scatter, an electron and
a proton can not combine to produce a H-atom,
(a) because of energy conservation
(b) without simultaneously releasing energy in the form of
radiation
(c) because
of momentum conservation
(d)
because of angular momentum conservation
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question_answer26)
The Bohr model for
the spectra of a H-atom
(a) will not be applicable to hydrogen in the molecular
form
(b) will
not be applicable as it is for a He-atom
(c)
is valid only at room temperature
(d)
predicts continuous as well as discrete spectral lines
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question_answer27)
The Balmer series
for the H-atom can be observed
(a) if we measure the frequencies of light emitted when an
excited atom falls to the ground state
(b) if we
measure the frequencies of light emitted due to transitions between excited
states and the first excited state
(c)
in any transition in a H-atom
(d)
as a sequence of frequencies with the higher frequencies getting closely packed
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question_answer28)
Let 
be the energy of the nth
level of H-atom. If all the H-atoms are in the ground state and radiation of
frequency 
/h falls on it,
(a) it will not be absorbed at all
(b) some of atoms will move to the first excited state
(c) all atoms
will be excited to the n = 2 state
(d)
no atoms will make a transition to the n = 3 state
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question_answer29)
The simple Bohr
modle is not applicable to He4 atom because
(a) He4 is an inert gas
(b) He4 has neutrons in the nucleus
(c) He4 has one more electron
(d) electrons are not subject to central forces
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question_answer30)
The mass of a H-atom is less than the sum of the masses
of a proton and electron. Why is this ?
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question_answer31)
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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question_answer32)
When an electron falls from a higher energy to a lower
energy level, the difference in the energies appears in the form of electromagnetic
radiation. Why can not it be emitted as other forms of energy?
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question_answer33)
Would the Bohr formula for the H-atom remain unchanged
if proton had a charge (+4/3) e and electron a charge (- 3/4) e, where e = 1.6
x 10-19 C. Give reasons for your answer.
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question_answer34)
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 orbital angular momentum according to the Bohr model ?
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question_answer35)
Positronium is just like a H-atom with the proton replaced
by the positively charged anti-particle of the electron (called the positron
which is as massive as the electron). What would be the ground state energy of
positronium?
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question_answer36)
Assume that there is no repulsive force between the
electrons in an atom but the force between positive and negative charges is
given by Coulomb's law as usual. Under such circumstances, calculate the ground
state energy of a He-atom.
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question_answer37)
Using Bohr model, calculate the electric current created
by the electron when the H-atom is in the ground state.
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question_answer38)
Show that the first few frequencies of light that are
emitted when electrons fall to the nth level from levels higher than n, are
approximate harmonics (i.e., in the ratio 1:2: 3....) when n»1.
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question_answer39)
What is the minimum energy that must be given to a H
atom in ground state so that it can emit an 
line
in Balmer series. If the angular momentum of the system is conserved, what
would be the angular momentum of such photon?
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question_answer40)
The first four spectral lines in the Lyman series of a
H-atom are 
, 
,
and
and 
if
instead of Hydrogen , we consider Deuterium, calculate the shift in the
wavelength of these lines.
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question_answer41)
Deuterium was discovered in 1932 by Harold Urey by
measuring the small change in wavelength for a particular transition in 1H
and 2H. This is because, the wavelength of transition depend to a
certain extent on the nuclear mass. If nuclear motion is taken into account, then
the electrons and nucleus revolve around their common centre of mass. Such a
system is equivalent to a single particle with a reduced mass (X, revolving
around the nucleus at a distance equal to the electron-nucleus separation. Here
where M is the nuclear mass and me
is the electronic mass. Estimate the percentage difference in wavelength for
the 1st line of the Lyman series in 1H and 2H. (Mass of 1H
nucleus is 1.6725 x 10-27 kg, Mass of 2H nucleus is 3.3374
x 10-27 kg, Mass of electron = 9.109 x 10-31 kg).
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question_answer42)
If a proton had a radius 5 and the charge was uniformly
distributed, calculate using Bohr theory, the ground state energy of a H-atom
when (i) 
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question_answer43)
In the Auger
process, an atom makes a transition to a lower state without emitting a
photon. The excess energy is transferred to an outer electron which may be
ejected by the atom. (This is called an Auger electron). Assuming the nucleus
to be massive, calculate the kinetic energy of an n = 4 Auger electron emitted
by Chromium by absorbing the energy from a n=2 to n=1 transition.
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question_answer44)
The inverse square
law in electrostatics is 
for the force
between an electron and a proton. The 
dependence
of I F I can be understood in quantum theory as being due to the fact that the
'particle' of light (photon) is mass less. If photons had a mass nip, force
would be modified to 
Estimate the
change in the ground state energy of a H-atom if mp-were 10-6
times the mass of an electron.
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question_answer45)
The Bohr model for
the H-atom relies on the Coulomb's law of electrostatics. Coulomb's law has not
directly been verified for very short distances of the order of angstroms.
Supposing Coulomb's law between two opposite charge + q1, - q2
is modified to
Calculate in such a case, the ground state energy of a
H-atom, if 
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