Difference between revisions of "Simulations of Particle Interactions with Matter"
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where <math>N(v) \Delta v</math> would represent the molesules in the gas sample with speeds between <math>v</math> and <math>v + \Delta v</math> | where <math>N(v) \Delta v</math> would represent the molesules in the gas sample with speeds between <math>v</math> and <math>v + \Delta v</math> | ||
− | ==== Example 1 What is the probability that an atom in a 12.011 gram block of carbon would have and energy of 5 eV? | + | ==== Example 1: P(E=5 eV) ==== |
+ | |||
+ | What is the probability that an atom in a 12.011 gram block of carbon would have and energy of 5 eV? | ||
First lets check that the probability distribution is Normailized; ie: does <math>\int_0^{\infty} P(E) dE =1</math>? | First lets check that the probability distribution is Normailized; ie: does <math>\int_0^{\infty} P(E) dE =1</math>? |
Revision as of 16:10, 31 August 2007
Overview
Particle Detection
A device detects a particle only after the particle transfers energy to the device.
Energy intrinsic to a device depends on the material used in a device
Some device of material with an average atomic number (
) is at some temperature ( ). The materials atoms are in constant thermal motion (unless T = zero degrees Klevin).Statistical Thermodynamics tells us that the canonical energy distribution of the atoms is given by the Maxwell-Boltzmann statistics such that
represents the probability of any atom in the system having an energy where
Note: You may be more familiar with the Maxwell-Boltzmann distribution in the form
where
would represent the molesules in the gas sample with speeds between andExample 1: P(E=5 eV)
What is the probability that an atom in a 12.011 gram block of carbon would have and energy of 5 eV?
First lets check that the probability distribution is Normailized; ie: does
?
is calculated by integrating P(E) over some energy interval ( ie: ). I will arbitrarily choose 4.9 eV to 5.1 eV as a starting point.
assuming a room empterature of
then
and
or in other words the precise mathematical calculation of calculating the probability may be approximated by just using the distribution function alone
This approximation breaks down as