Problem Based
Learning in Basic Physics - VI
School Science 51(3) Sept 2013
A. K .Mody
V. E.S. College of Arts, Science and
Commerce, Sindhi Society
Chembur, Mumbai – 400 071
H. C. Pradhan
HBCSE, TIFR, V. N. Purav Marg,
Mankhurd
Mumbai – 400 088
In this article- sixth in the series of articles we
present problems for a problem based learning course from the area of quantum
physics and nuclear physics. We present the learning objectives in this area of
basic physics and what each problem tries to achieve with its solution.
In this article, sixth in the series of Problem Based Learning in Basic Physics, we present problems on Quantum Physics and Nuclear Physics. Methodology and philosophy of selecting these problems are already discussed. (Pradhan 2009, Mody 2011)
To review methodology in brief, we
note here that this PBL (Problem Based Learning) starts after students have
been introduced to formal structure of Physics. Ideally students
would attempt only main problem. If they find it difficult, then depending upon
their area of difficulty, right auxiliary problem have to be introduced by
teacher who is expected to be a constructivist facilitator. Teacher may choose
as per his/her requirement or may construct questions on the spot to guide
student to right idea and method.
Problems on Quantum Physics
Learning
Objectives:
1.
Exposure
to quantum idea.
2.
Planck
and Einstein equation.
3.
Bohr’s
theory of hydrogen atom and emission of spectral lines.
4.
Calculation
to get an idea of magnitude of quantities involved.
Problems:
1. A
beam of light has three wavelengths 4144 Ao, 4972Ao, and
6216 Ao with a total intensity of 3.6´10 –3
W/m2 equally distributed amongst the three wavelengths. The beam
falls normally on an area of 10 cm2 of a clean metallic surface of
work function 2.3 eV. Assume that there is no loss of light by reflection and
that each energetically capable photon ejects one electron. Calculate the
number of photoelectrons liberated in two seconds.*
·
This
problem needs to use photoelectric equation to find which of the wavelength can
induce photoelectric emission. It requires to calculate flux of photon (number
of photons incident) of each wavelength to find number of electrons emitted, by
using Planck’s quantum hypothesis.
Tasks involved
in this problem are:
a.
To find which
of the wavelength is above threshold to be rejected.
b.
To calculate
number of photons incident corresponding to each wavelength using given
information and Planck’s quantum hypothesis.
c.
To find
number of electrons emitted as per Einstein’s photoelectric equation.
2. Consider
a potassium surface that is 75 cm away from a 100 W bulb. Suppose that the
energy radiated by the bulb is 5% of the input power. Treating each potassium
atom as a circular disc of diameter 1 A°, determine the
time required for each atom to absorb an amount of energy equal to its work
function of 2.0 eV, according to the wave interpretation of light.*
- This problem involves estimation of time required for photoelectric emission on the basis of classical theory.
- Since calculation of this problem contradicts observation it illustrates need for new (quantum) theory.
Tasks involved
in this problem are:
a. To
calculate the amount of energy received by an atom per second from geometrical
consideration from given data.
b. To
calculate time using given data of energy required for emission of electron.
3. A
hydrogen atom is excited from a state with n=1 to a state with n=3.
Calculate (a) the energy absorbed
by the atom, and (b) the wavelengths of the spectral lines emitted when the
atom returns from n=3 to n=1 state. Display the lines emitted on an energy
level diagram.
- This problem involves simple calculation based on Bohr’s theory and understanding of possible paths for de-excitation of electron.
Tasks involved
in this problem are:
a. To
calculate energy needed to excite H-atom to 3rd energy level.
b. To
recognize all the possible paths available to return to ground state.
c. To
calculate wavelengths emitted in the process.
d. To
draw and show transitions on energy level diagram.
Problems
on Nuclear Physics
Learning
Objectives:
- To become familiar with law of radioactive decay and nuclear energy.
- Application of radioactivity.
- Nuclear energy calculation. How important it is.
Problems:
- Assume when the planet Earth was formed, U238 and U235 were present in equal abundance. At present, the ratio of their abundance is 140:1. If their half-lives are 4.5´109 years and 7.13´108 years respectively, estimate the age of the Earth. *
- This is a problem of uranium dating and involves use of simple radioactive exponential decay law.
- It allows order of magnitude prediction of age of earth.
Tasks involved
in this problem are:
a. To
write equation for radioactive decay for each species of uranium.
b. To
estimate time lapsed assuming both the species were equally abundant initially
using their present proportion.
- A small quantity of solution containing Na24 radio nuclide (half-life 15 hours) of activity 1.0 mcurie is injected into blood of a person. A sample of the blood of volume 1cc taken after 5 hours shows an activity of 296 disintegrations per minute. Determine the total volume of blood in the body of the person. Assume that the radioactive solution mixes uniformly in the blood of the person. (1 curie = 3.7´1010 dps) [JEE 1993]
- This problem also involves simple exponential decay but this time for medical application.
Tasks involved
in this problem are:
a. To
understand here that the activity will vary not only with time but also with
sample of blood.
b. To
estimate total volume of blood from the sample using exponential decay of
activity and volume dependency.
- In the interior of the sun a continuous process of 4 protons, fusing into helium nucleus and a pair of positrons is going on. Calculate
i.
The release of energy per process.
ii.
If the sun radiates an energy of about
4×1026 J/s, how much mass gets converted into helium every second?
iii.
If mass of the sun is 2×1030
kg, estimate the time it will take to convert all the mass into helium.
iv.
The sun has been in its present stable
state for 5×109 yrs, how many more years it will continue to shine
in this stable state? Neglect the energy carried away by neutrinos.
Given: m (1H1) = 1.007825
amu, m (2He4)
= 4.002603 amu,
me = mb+ = 5.5´10-4
amu; 1 amu = 931.5 MeV
·
This
problem involves simple energy calculation in nuclear processes and estimation
(order of magnitude) of life of the Sun.
Tasks involved
in this problem are:
a.
To calculate
energy released per process.
b.
To calculate
mass of hydrogen consumed from solar luminosity.
c.
To calculate
time required for sun to burn all its hydrogen and hence estimate its life.
4. It
is proposed to use the nuclear fusion reaction 1H2 + 1H2
®
2He4 in a nuclear reactor of 200 MW rating. If the energy
from the above reaction is used with 25% efficiency in the reactor, how many
gram of deuterium fuel will be needed per day. [The masses of 1H2
and 2He4 are
2.0141 amu and 4.0026 amu respectively.]*
- This problem is similar as the problem 3. Its importance is from the point of view of Nuclear power generation.
Tasks involved
in this problem are: Similar to that in
problem 3 above.
Solutions:
Quantum
Physics:
1. Photoelectric Effect :
I
= 3.6´10-3
W/m2 distributed equally
amongst three wavelengths
\Each
will be 1.2´10-3
W/m2 and W0 = 2.3
eV
l1
= 4144 Ao corresponding
energy E1 = hc/l1
= 2.999 eV
l2
= 4972 Ao corresponding
energy E2 = hc/l2
= 2.500 eV
l1
= 6216 Ao corresponding
energy E3 = hc/l3
= 1.990 eV
Thus
only first and second wavelengths will be able to knock electrons off.
Thus
in 1 sec (from 10 cm2) l1
will be able to eject N1 =
=2.5´1012
electrons
and l2
will be able to eject N2 =
=6.0´1012
electrons
Total
number of electrons emitted in 2 sec = 2 (N1 +N2)
2. Photoelectric Effect in
Classical Domain:
Input
power : P, fraction of input
power radiated: f , Work function of the metal : W0:
Diameter
of the atom :D,
Distance of atom from the bulb : d
\time
required for emission Dt
=
3. Bohr Theory :
In transition from n =
3 to n = 1 there are three possible wavelengths that can be emitted.
l3®1
= 6577 Ao , l3®2
= 1028 Ao and l2®1 = 1219 Ao
Nuclear Physics
1.
Radioactive Dating :
N0 (U238) = N0
(U235) but N (U238) : N (U235) = 140 : 1
T½ (U238)
= 4.5´109
years and T½
(U235) = 7.13´108 years
T½ = 0.693/l
N = N0 e-lt Þ
= 6.04´109 years
2.
Medical Application of Radioactivity:
Activity
A = dN/dt , A = A0
e-lt and
T½ = 0.693/l
A0 = 3.7´104
dps and T½
= 15 hrs
Let V be total volume of blood and
v = 1 cc : sample
After t = 5 hrs a = 296 dpm in volume v whereas A = 2.937´103
dps
\
V = v(A/a) = 5953 cc = 5.953 litre
3.
Nuclear Fusion in the Sun:
(i)
Release of energy per process = mass
excess = 25.7066 MeV
(ii)
Total energy ¸
energy per process = no. of processes
per sec = 9.725´1037 /sec
Mass
converted into Helium = no. of processes ´ m(2He4)
= 6.5´1011
kg/sec
(iii)
Time to convert all mass into Helium at
this rate = mass of the sun ¸
rate of He production = 1.886´1011
years
(iv)
1.886´1011
years - 5´109
years =
1.836´1011
years
4.
Nuclear Fission in a Nuclear Reactor:
Energy per reaction = mass
excess =
23.8464 MeV
200 MW at 25% efficiency means the total
energy produced must be 800 MW
This requires 800 MW ¸ 23.8464
MeV = 2.0968´1020
reaction
Number of deuterium atoms required per
second = 2´2.0968´1020
= 4.194´1020
This translates to 1.402´10-6
kg per second or 0.1211 kg per day.
References:
* Source unknown
- JEE - Joint Entrance Examination for admission to IIT
- Mody A. K. &Pradhan H. C., ‘Problem Based Learning in Basic Physics – I, School Science 49 (3) Sept 2011
- Pradhan H.C. &Mody A. K., ‘Constructivism applied to physics teaching for capacity building of undergraduate students’, University News, 47 (21) 4-10, (2009)
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