# Chapter 12: Atoms

12.1 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.)

12.2 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?

12.3 What is the shortest wavelength present in the Paschen series of

spectral lines?

12.4 A difference of 2.3 eV separates two energy levels in an atom. What

is the frequency of radiation emitted when the atom make a

transition from the upper level to the lower level?

12.5 The ground state energy of hydrogen atom is –13.6 eV. What are the

kinetic and potential energies of the electron in this state?

12.6 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.

12.7 (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.

12.8 The radius of the innermost electron orbit of a hydrogen atom is

5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?

12.9 A 12.5 eV electron beam is used to bombard gaseous hydrogen at

room temperature. What series of wavelengths will be emitted?

12.10 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 × 1011 m with orbital speed 3 × 104m/s. (Mass of earth = 6.0 × 1024 kg.)

ADDITIONAL EXERCISES

12.11 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?

12.12 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.

12.13 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.

12.14 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 (~ 10–10m).

(a) Construct a quantity with the dimensions of length from the

fundamental constants e, me, 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 recognizing that h, me, and e will yield the right atomic

size. Construct a quantity with the dimension of length from h,

me, and e and confirm that its numerical value has indeed the

correct order of magnitude.

12.15 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?

12.16 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?

12.17 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 (μ– ) of mass about 207me orbits around a proton].

### Related Posts

### Leave a Reply Cancel reply

**Error:** Contact form not found.