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**Exercise : ** Solutions of Questions on Page Number : **435**

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Q1 :
**
**

Choose the correct alternative from the clues given at the 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.)

**Answer :**

**(a)** The sizes of the atoms taken in
Thomson's
model and
Rutherford's
model have the same order of magnitude.

**(b)** In the ground state of
Thomson's
model, the electrons are in stable equilibrium. However, in
Rutherford's
model, the electrons always experience a net force.

**(c)** A *classical* atom based on
Rutherford's
model is doomed to collapse.

**(d)** An atom has a nearly continuous mass distribution in
Thomson's
model, but has a highly non-uniform mass distribution in
Rutherford's
model.

**(e)** The positively charged part of the atom possesses most
of the mass in both the models.

Answer needs Correction? Click Here

Q2 :
**
**

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 temperatures below 14 K.) What results do you expect?

**Answer :**

In the alpha-particle scattering experiment, if a thin sheet of
solid hydrogen is used in place of a gold foil, then the
scattering angle would not be large enough. This is because the
mass of hydrogen (1.67 x
10^{-27}
kg) is less than the mass of incident
α-particles
(6.64 x
10^{-27}
kg). Thus, the mass of the scattering particle is more than the
target nucleus (hydrogen). As a result, the
α-particles
would not bounce back if solid hydrogen is used in the
α-particle scattering experiment.

Answer needs Correction? Click Here

Q3 :
**
**

What is the shortest wavelength present in the Paschen series of spectral lines?

**Answer :**

Q4 :
**
**

A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level?

**Answer :**

Q5 :
**
**

The ground state energy of hydrogen atom is -13.6 eV. What are the kinetic and potential energies of the electron in this state?

**Answer :**

Q6 :
**
**

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 the photon.

**Answer :**

Q7 :
**
**

(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.

**Answer :**

Q8 :
**
**

The radius of the innermost electron orbit of a hydrogen atom is
5.3
x 10^{-11}
m. What are the radii of the *n* = 2 and *n* =3 orbits?

**Answer :**

Q9 :
**
**

A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?

**Answer :**

Q10 :
**
**

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 10^{11} m with
orbital speed 3 x
10^{4} m/s. (Mass of earth = 6.0
x 10^{24} kg.)

**Answer :**

Q11 :
**
**

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
*α***-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 *α*-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
*α*-particles scattered at
moderate angles is proportional to *t*. What clue does this
linear dependence on *t* provide?

**(d)** In which model is it completely wrong to ignore
multiple scattering for the calculation of average angle of
scattering of *α*-particles by a
thin foil?

**Answer :**

Q12 :
**
**

The gravitational attraction between electron and proton in a
hydrogen atom is weaker than the coulomb attraction by a factor
of about
10^{-40}.
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.

**Answer :**

Q13 :
**
**

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.

**Answer :**

Q14 :
**
**

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
simulate 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 (~
10^{-10}
m).

**(a)** Construct a quantity with the dimensions of length
from the fundamental constants *e*,
*m*_{e}, and *c*. Determine its
numerical value.

**(b)** You will find that the length obtained in (a) is 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 *h*,
*m*_{e}, and *e* will yield the right
atomic size. Construct a quantity with the dimension of length
from *h*, *m*_{e}, and *e* and
confirm that its numerical value has indeed the correct order of
magnitude.

**Answer :**

Q15 :
**
**

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?

**Answer :**

Q16 :
**
**

If Bohr's
quantisation postulate (angular momentum =
*nh/*2π) 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?

**Answer :**

Q17 :
**
**

Obtain the first
Bohr's radius
and the ground state energy of a *muonic* *hydrogen
atom* [i.e., an atom in which a negatively charged muon
(ÃŽÂ¼^{-})
of mass about 207m_{e} orbits around a proton].

**Answer :**

Physics Part 2 - Physics : CBSE ** NCERT ** Exercise Solutions for Class 12th for ** Atoms ** will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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- Chapter 2 - Electrostatic Potential And Capacitance Class 12
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