Physics 215 Spring 2016
Homework #12
1. What are the number of neutrons and protons for the following nuclides:
might have to look up Z in Appendix B of B&W.
,
,
,
? You
2. What is the ratio of density of the nucleus to that of water?
3. (a) Show that t
Physics 215
Homework Set 1
1. A spaceship of length 40m at rest is observed to be 20m long when in motion. How fast is it moving?
Hint: derive a formula giving in terms of and put it on your formula sheet.
2. The Concorde travelled 8000 km between two pla
Physics 215 Spring 2016
Homework #3
1. A particle having a speed of 0.92 c has a momentum of 10
MeV /c2 units?
. What is its mass a) in kg, and b) in
2. Calculate the momentum, kinetic energy, and total energy of an electron traveling at a speed of (
Physics 215 Spring 2016
Homework #13
1. Supply the missing neutrinos in the following reactions or decays.
(a)
?
(d)
?
(b) ?
(e) ?
?
(c)
2. Explain why each of the following reactions is forbidden.
(a)
(b)
3. Determine the
Physics 215 Spring 2016
Homework #8
1. Show directly that the trial wave function ,
2.
Choose A to normalize the wave function
satisfies the Schrdinger Equation.
from r = 0 to where
and A are constants.
3. . A wave function has the value A sin x bet
Physics 215 Spring 2016
Homework #10
1. Compare the wavelength of a particle when it passes a barrier of height (a) + and (b)
E > | |. Calculate the momentum and kinetic energy for both of these cases algebraically.
where
2 . (a) Calculate the transmissio
Physics 215 Spring 2016
Homework #4
1. Gold has a molar mass of 197 g/mol. (a) How many moles of gold are in a 2.50 g sample of
pure gold? (b) How many atoms are in the sample?
2. The best laboratory vacuum has a pressure of about 1.00 x 10-18 atm, or 1.0
Physics 215 Spring 2016
Homework #9
1 The wave function for the ground state for the simple harmonic oscillator is
. Normalize
the wave function to find the value of the constant A. Determine , and
= .You will
need some Gaussian integralssee the referen
Physics 215 Spring 2016
Homework #7
1. An atom in an excited state of 4.7 eV emits a photon and ends up in the ground state. The lifetime of the
s. (a) What is the energy uncertainty of the emitted photon? (b) What is the
excited state is 1.0 X 10
spectra
Physics 215 Spring 2016
Homework #5
1.
Calculate max for blackbody radiation for a) liquid helium (4.2K), (b) room temperature (293K), (c) a
steel furnace (2500K), and (d) a blue star (9000K)
2.
How many photons per second are contained in a beam of total
Physics 215 Spring 2016
Homework #6
X rays scattered from a crystal have a first-order diffraction peak at
higher-order peaks appear?
1.
12.5 . At what angle(s) will
Calculate the de Broglie wavelength of a 1.2-kg rock thrown with a speed of 6.0 m/s into
Physics 215
HW11
Spring 2016
1. Internal magnetic fields acting on electrons in an atom can be of order .3 T. Lets
estimate the size of their effect. For hydrogen atoms in a 4d state, what is the maximum
difference in potential energy between atoms when p
Physics 215
Homework 4 Solutions
1. a) 2.50g of gold corresponds to 2.50g/(197 g/mol)=0.0127 mol.
b) 0.0127 moles 6.022 1023 atoms/mole = 7.65 1021 atoms.
2. The Ideal Gas Law, pV = NkBT, can be rewritten as
N
p
1.01 10 13 Pa
2.50 10 7 m 3 25.0 cm 3
- 23
"
This module implements Pauli algebra by subclassing Symbol. Only algebraic
properties of Pauli matrices are used (we don't use the Matrix class).
See the documentation to the class Pauli for examples.
References
~
. [1] http:/en.wikipedia.org/wiki/Pauli
r"
Wigner, Clebsch-Gordan, Racah, and Gaunt coefficients
Collection of functions for calculating Wigner 3j, 6j, 9j,
Clebsch-Gordan, Racah as well as Gaunt coefficients exactly, all
evaluating to a rational number times the square root of a rational
number
from _future_ import print_function, division
from sympy import factorial, sqrt, exp, S, assoc_laguerre, Float
def R_nl(n, l, r, Z=1):
"
Returns the Hydrogen radial wavefunction R_cfw_nl.
n, l
r
Z
quantum numbers 'n' and 'l'
radial coordinate
atomic numbe
"
Physical units and dimensions.
The base class is Unit, where all here defined units (~200) inherit from.
The find_unit function can help you find units for a given quantity:
> import sympy.physics.units as u
> u.find_unit('coul')
['coulomb', 'coulombs']
from _future_ import print_function, division
from sympy.core import S, pi, Rational
from sympy.functions import assoc_laguerre, sqrt, exp, factorial, factorial2
def R_nl(n, l, nu, r):
"
Returns the radial wavefunction R_cfw_nl for a 3d isotropic harmonic
Physics 215
Homework #7
1. An atom in an excited state of 4.7 eV emits a photon and ends up in the ground state. The lifetime of the
s. (a) What is the energy uncertainty of the emitted photon? (b) What is the
excited state is 1.0 X 10
spectral line width
Physics 215
Homework 6 Solutions
1.
We can also find 4 = 59.7, but there is no solution for n > 4 because 5sin 1 > 1.
2.
3.
4.
And for LHC: multiply by 1/7 = 1.77 E-19 m (first K2 term dominates)
5.
6.
7. bacterium velocity uncertainty
8. Hydrogen line in
Physics 215
Homework 3 Solutions
1. a) Find mass of given speed and momentum
b) since 1eV = 1.6 10-19 J, 1MeV/c2 = 1.6 10-13 kg (m/s)2 / (3 108m/s)2= 1.78 10-30 kg
m = 1.42 10-25 kg x 1 MeV/c2 / 1.78 10-30 kg = 7.98 104 MeV/c2=79.8 GeV/c2
2. m = 511 keV/c
Physics 215
Homework 5 Solutions
1.
2. number of photons for number of watts
3. threshold wavelength and KE if wavelength halved
Or: since the photon energy at threshold is 4.64, doubling the photon energy will leave 4.64eV more
available for kinetic ener
Physics 215
Homework #3
1. A particle having a speed of 0.92 c has a momentum of 10
MeV /c2 units?
. What is its mass a) in kg, and b) in
2. Calculate the momentum, kinetic energy, and total energy of an electron traveling at a speed of (a) 0.20c,
an
Physics 215
Homework #2
1.
Alice and friends are riding on a train Names Flora, Feng indicate Front; Rose, Roberto indicate Rear.
Here is one solution, using Mermins Eq 5.5, ct = x , or cT= D. Note that T and D must be the same
frame. I will follow with a
"
Second quantization operators and states for bosons.
This follow the formulation of Fetter and Welecka, "Quantum Theory
of Many-Particle Systems."
"
from _future_ import print_function, division
from collections import defaultdict
from sympy import (Add