Problem 19.16 Suppose you are holding your hands in front of you, 10 cm
apart.
(a) Estimate the total number of electrons in each hand.√(b) Estimate the total repulsive force of all the electrons in one hand
on all the electrons in the other.√(c) Why don’t you feel your hands repelling each other?
(d) Estimate how much the charge of a proton could differ in mag-
nitude from the charge of an electron without creating a noticeable
force between your hands.
17 Potassium 40 is the strongest source of naturally occurring
beta radioactivity in our environment. It decays according to(^40) K→ (^40) Ca +e−+ ̄ν.
The energy released in the decay is 1.33 MeV, where 1 eV is defined
as the fundamental chargeemultiplied by one volt. The energy
is shared randomly among the products, subject to the constraint
imposed by conservation of energy-momentum, which dictates that
very little of the energy is carried by the recoiling calcium nucleus.
Determine the maximum energy of the calcium, and compare with
the typical energy of a chemical bond, which is a few eV. If the
potassium is part of a molecule, do we expect the molecule to sur-
vive? Carry out the calculation first by assuming that the electron
is ultrarelativistic, then without the approximation, and comment
on the how good the approximation is.
18 Several pointlike, interacting particles are released, all ini-
tially at rest, within the same finite region of space. We want to
know whether, without violating conservation of energy, it is pos-
sible for one of these particles to be ejected to an infinite distance,
while the others stay within the original region. Consider this ques-
tion for each of the following systems. (a) Two particles of mass
m, interacting gravitationally. (b) Three such particles. (c) Two
particles, both with chargeq. (d) Chargesqand−q. (e) Chargesq,
q, and−q.
19 As shown in the figure, a particle of massmand charge
qhangs from a string of length, forming a pendulum fixed at a central point. Another chargeqis fixed at the same distance,
directly below the center. Find the equilibrium values ofθ and
determine whether they are stable or unstable.
Key to symbols:
√easy typical challenging difficult very difficult
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Problems 527