Physics 249 Homework 1
Due Sep 14th
1) Based on 3.2
Consider electrons and antiprotons entering a uniform field B perpendicular to their
direction of flight and traversing a length l I that field.
Show that the electrons or antiprotons are deflected through angle 𝜃 = 𝑒𝑙𝐵/𝑚𝑣 for small
l and nonrelativistic speed.
a) For B=8.00x10-5T, l =1.00x10-2m, v = 3.00x106 m/s find the displacement on a
wall 1m away compared to a path without the field B.
b) Given a resolution of 1mm on the displacement measurement and assuming the
other quantities in the formula are measured with perfect accuracy can the
electron and proton by distinguished based on their displacement?
c) What accuracy can the electron mass be measured with in this experiment.
A diagram of the transition through the magnetic field.
𝑠
𝑙
Since l is small theta should be small. For small values of theta s=l and 𝜃 = 𝑟 = 𝑟
The magnetic force provides the centripetal force: evB = mv2/r, r = mv/eB
𝑙
The 𝜃 = 𝑟 =
𝑒𝐵𝑙
𝑚𝑣
Displacement 𝑑 = 𝜃𝐿 =
𝑒𝐵𝑙
𝑚𝑣
𝐿
Given the electron mass 9.109382x10-31 kg and the antiproton mass 1.672622x10-27 kg
and e = 1.602176 x10-19 C
Then
electron d: 0.0469m
antiproton d: 2.55x10-5 m
On an event by event basis due to the measurement error electron may be mistaken for
protons and the fraction of a percent level. Given a small number of repetitions of the
experiment they can easily be distinguished since the electron are will be displaced by 2.9
mm with 1mm resolution compared to the protons which will not be displaced
significantly.
Assuming the other quantities in the problem are well measured the largest error is on the
displacement measurement. The accuracy of an individual mass measurement will be
about 2.1%. It should be easily possible to tell the electron from an antiproton. Given
many measurement of individual electron you should be able to achieve substantially
better than 2.1% by averaging them which will improve in accuracy as 1/root(N) where N
is the number of measurement.
2) 3.18
Calculate the average energy per mode of oscillation for a long wave length 𝜆 =
10ℎ𝑐/𝑘𝑇 and a short wavelength 𝜆 = 0.1ℎ𝑐/𝑘𝑇 based on the quantum formula and
compare your result with the classical expectation kT. Express your answers as numbers
times kT.
3) 3.32
The longest wavelength of light that will cause emission of electrons from cesium is
653nm.
a) Compute the work function for cesium.
b) If the light of 300nm were to shine on cesium, what would be the energy of the
ejected electrons.
Give answers in units of eV
A very useful relation is hc=1240eVnm
4) Based on 3.46
In his first e/m experiment Thomson measured q/m of the electrons by collected them in
an insulated beam stopper and measuring the total collected charge Q and the temperature
rise deltaT in the beam stopper (known as calimetric energy measurement). Derive a
formula for q/m in terms the specific heat, c, and the mass, M, of the beam stopper, the
velocity of the electrons and the measured values.
The total charge collected is: Q=Ne
The total energy absorbed is: 𝑁𝐾𝐸 = 𝑁
Solving for N and equating:
𝑄
𝑒
=
𝑚𝑣 2
2𝑐𝑀Δ𝑇 𝑒
𝑚𝑣 2
2
= 𝑐𝑀Δ𝑇
𝑄𝑣 2
, 𝑚 = 2𝑐𝑀Δ𝑇
5) 3.56
Estimate the time lag (expected classically but not observed) for the photoelectric effect.
Assume a point source emits 1W of light energy uniformly in all directions. For an atom
with a work function of 2eV at a distance of 1m how long does it take for the required
energy to be absorbed? Assume a reasonable size for the atom and that all energy hitting
the atom is absorbed.