Modern Physics
Homework #2
Modern Physics 3rd Ed. Serway, Moses, and Moyer- Chapter 2 #11, 17, 23
4.
During an experiment, scientists obtain the following results for the lifetime of a
particle in microseconds:
58, 61, 63, 68, 69, 71, 71, 72, 72, 74, 75, 76, 77, 78, 79, 79, 79, 80, 82, 82,
86, 91, and 98
A.
B.
Calculate the mean lifetime of the particle.
Calculate the standard deviation.
Show all work (Don’t just give me the result)!!
5.
Show that the full-width at half-maximum (  ) of a Gaussian distribution is given
by
Γ  2 2 Ln(2) σ  2.35 σ
where  is the standard deviation of the Gaussian distribution.
6.
Estimate the probability of getting heads exactly 500 times in 1000 unbiased flips
of a coin.
7.
A) Determine the typical speed of a thermal neutron at room temperature (i.e. a
neutron whose kinetic energy is equal to kT). B) At what temperature is the
typical neutron speed equal to 1% of the speed of light?
8.
For protons on the surface of the sun ( T = 6000 K ) estimate A) the average
kinetic energy and B) the most probable speed.
9.
The average speed of the molecules of a certain gas at room temperature is 440
m/s. Identify the gas.
10.
Consider a gas of nitrogen molecules in thermal equilibrium at room temperature.
What fraction of the molecules have an x-component of the velocity within the
range
 0.01 Vrms  Vx  0.01 Vrms
where Vrms is the root-mean-square value of Vx?