Physics Facts Flashcards
Force =
M * A (F = force; M = mass; A=acceleration)
1 Joule =
1 kg m2/s2 = 1 Newton-meter
Kinetic Energy
(m * v2)/2 (m = mass in Kg; v = velocity (m/s))
Potential Energy
m * g * h (m = mass in kg; g = gravitational acceleration; h = height above floor)
Atomic Number (Z)
of protons in nucleus of atom
Atomic mass number (A)
of protons + neutrons in nucleus of atom
Compare the following particles in terms of Mass, Rest Energy (MeV), and Charge
Particle Mass (kg) Rest Energy (MeV) Charge (e) *
Electron 9.11 x 10^-31 0.511 -1
Positron 9.11 x 10^-31 0.511 +1
Proton 1.67 x 10^-27 938.2 +1
Neutron 1.68 x 10^-26 939.5 0
Alpha 6.65 x 10^-27 3729 +2
* unit of charge is 1.6 x 10-19 coulomb
Electron volt (eV):
kinectic energy gained by electron after being accelerated through a potential difference of one volt
1eV = 1.6021 * 10-12 ergs = 1.6021 * 10-19 joules = 3.83 * 10-20 cal
(remember that joules = (Kg * m2)/ s2))
Alpha Particle:
helium nuclei (2 protons + 2 neutrons)
Beta minus particle
electron emitted by nucleus
Beta plus particle
positron emitted by nucleus (same mass as electron but with a +charge)
Neutron
part of nucleus of atom (has no charge)
Gamma ray
X-ray emitted from nucleus
Speed of light (in vacuum):
3 x 108 m/s
What is the relationship between wavelength, frequency (v) in Hz, speed of light (c):
Speed of light (c) = wavelength * frequency (v)
or Wavelength = speed of light/frequency
or Frequency (v) = speed of light (c)/ wavelength
Example: What is the frequency of a photon with a wavelength 15 * 10-11m
Frequency (v) = (3 * 108 m/s) / (15 x 10-11m) = 2 * 1018 Hz
Example: What is the wavelength of the typical EM waves used to accelerate electrons in a linear accelerator (typically frequency of 3000 MHz)?
Wavelength = (3 * 108 m/s)/(3 * 109 Hz) = 0.1m or 10cm
Hz is cycles per second.
Energy of Photon:
E= hv (E = energy of photon; v= frequency of photon, h = Planck’s constant = 6.626 x 10^-34 joules-second)
or **v = E/h **
or E= hc/wavelength (since Frequency (v) = speed of light (c)/ wavelength)
Example: What is the energy of a photon with wavelength 15 * 10-11m?
E = (1.24 * 10-12 MeV*m) / (15 x 10-11 m) = 0.0083 MeV
(remember that hc = 1.24 * 10-12 MeV*m because h = 6.626 *10-34 joules * second or 4.136 * 10-15 eV * second and c = 3 * 108 m/s; remember to multiply eV * 10-6 to get to MeV!!!)
Wavelength formula
Wavelength = speed of light (c)/frequency (v)
or Wavelength = speed of light (c)/(E/h)
so Wavelength = hc/E (hc = 1.24 * 10-12 MeV*m)
Example: What is wavelength of 100 keV photon? Wavelength = (1.24 \* 10<sup>-12 </sup>MeVm)/0.1 MeV) = **1.24 \* 10<sup>-11</sup>**
Characteristic x-ray
photon given off when outer orbit electron moves to fill a inner electron shell vacancy caused by an incoming electron causes ionization of an atom
Bremsstrahlung (braking radiation):
produced when incoming electron interacts with positive charge of the atomic nucleus
source of most x-ray production
energy lost by incoming electron is given off as a photon
Bremsstrahlung production efficiency = (electron energy in eV) * (atomic # of target) * 10-9
At diagnostic energies (<120keV) bremsstrahlung efficiency is ~1%, At therapeutic MV energies it is 15-50%!
Thoraeus filter
Tin (closest to x-ray tube) →copper → aluminum
used to harden orthovoltage beams (characteristic x-ray of aluminum is only 1.5keV and is absorbed by air before hitting patient)
Calculate electron energy conversion to photon energy
F = 3.5 * 10-4 ZE (Z = atomic #; E = maximum energy of electrons in MeV)
Calculate Beam Intensity Transmission
T = I/I0
Beam Attenuation (single energy source)
I = Ioe-µx (x = thickness of filter; µ = linear attenuation coefficient (a function of filter material and energy of photon beam))
Example: Initial intensity = 2000 photons, µ= 0.2mm-1, thickness = 3mm
I = 1098 photons
Linear attenuation coefficient
= µ
- probability that a given photon will be attenuated in a unit thickness of a particular attenuator
- varies with photon energy and filter composition (atomic number, Z)
-a larger number (closer to 1.0) indicates a higher probability of photon attenuation
The CT number (in Hounsfield units) = 1000 x [(umaterial - uwater)/uwater where u = the linear attenuation coefficient