Physics 102
Homework set 11
Solutions
L. Weinstein

Exercises:
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31.34: The slower electron has the longer wavelength.  lambda = h/p =
h/mv.  The larger v is, the smaller lambda is.

31.47: Heisenberg's uncertainty principle does not apply here because
it is possible to devise  a way to measure air pressure without
letting any air escape.  It also does not apply here because it
applies to the simultaneous measurement of two quantities such as
position and momentum or energy and time.

32.2: A blue photon has a higher frequency and hence a higher energy
than a red one.  Therefore it results from a greater energy
transition.

32.8: If an electron in a hydrogen atom obeyed classical mechanics,
then hydrogen would have a continuous spectrum.  The line spectrum
occurs because electrons can only occupy specific discrete orbits so
that there are only certain energy differences between orbits.  These
energy differences are the allowed energies of emitted photons.  If
the electrons obeyed classical mechanics, then they could occupy any
orbit with any energy.


32.14: The photoelectric effect is best explained by the particle
nature of the electron.  Photons knock out single electrons.  You
cannot knock out a fraction of an electron.

The discrete levels in the Bohr model are best explained by the wave
nature of electrons.  The electron orbits correspond to standing waves
of the electron in a circle around the nucleus.


33.2: X-rays and gama rays are both electromagnetic radiation.


33.4: The atoms of the radioactive material are unstable.  When they
decay, they release energy.  Part of that energy is converted to the
thermal energy of the sample.


33.8: A gamma ray is uncharged and will not be deflected by the
electric field.  An alpha particle has a positive charge and will be
deflected in the direction of the field lines.  A beta particle has a
negative charge and will be deflected in the opposite direction to the
field lines.


33.16: The repulsion comes from the electric force between the two
protons.  The attraction comes from the nuclear force between the two
protons.


33.20: A positively charged hydrogen atom is a proton.  A neutral H
atom has one proton and one electron.  To make it positively charged,
you must remove the electron.


33.22: Inverse square law: If it registers 360 counts per minute (cpm)
at a distance of 1 m, then it will register 360/2^2 = 90 cpm at a
distance of 2 m and it will register 360/3^2 = 40 cpm at a distance of
3 m.


Problems:
--------------------

33.2: In order to decrease from 160 counts per minute (cpm) to 10 cpm,
it must have halved four times (160 -> 80 -> 40 -> 20 -> 10).
Therefore, four half-lives have elapsed in 8 hours.  Therefore, the
half life of the material is 2 hours.


Estimation:
---------------------

We are about 70 km from Surrey.  This means that the neutrinos from
Surry are spread out over the surface of a sphere of radius 70 km.
This sphere has area A = 4 pi r^2 = 4 * 3 * (7*10^4 m)^2 = 6*10^10
m^2.  The surface area of the front of my body is about 1 m^2 (about 2
m tall by 0.5 m wide).  This means that the number of neutrinos
passing through my body from Surry every second is:

N = 4*10^20 neutrinos/second * 1 m^2 / 6*10^10 m^2 = 6*10^9
neutrinos/second.

Wow! That's a lot!