Chapter 10 - creating models Flashcards
What is a model?
A set of assumptions which simplifies and idealises a problem
Why are models useful?
They allow you to write equations and make calculations and predictions for a particular situation, without having too many factors to consider.
One model can often be extended or changed so that it can be applied to a different process.
What makes an atom unstable/radioactive?
Too many neutrons, too many protons or too much energy in the nucleus
What is radioactive decay?
When atoms release energy and/or particles until they reach a stable form
What is meant by radioactive decay being a random process?
You can’t tell which atom will decay next or when a given atom will decay, you can only work with averages
The decay is unaffected by any external condition such as temperature
What can radioactivity be modelled by?
Exponential decay
When can a random process be predicted using a model?
With a large enough sample (ie, number of atoms) the overall behaviour shows a pattern, so can be predicted with a model
What can an exponential decay model for radioactive decay let you predict?
The number of atoms which will decay in a given period of time (eg one second)
NOT when an individual atom will decay
What is activity?
The number of unstable atoms which decay per second
What is the activity of a sample proportional to?
The size of the sample
What makes something exponential decay?
The rate of change of a quantity is proportional to the size of that quantity
What is the decay constant?
The probability of a given nucleus decaying in any given second
What are the units of the decay constant?
s^-1
What is the symbol for the decay constant?
λ
What is activity?
The number of unstable atoms which will decay in a second
What is the symbol for activity?
A
What is the equation for activity?
A = λN Activity = decay constant x number of radioactive nuclei remaning in the sample
In radioactive decay, what is N?
The number of radioactive nuclei remaining in the sample
What are the units of activity?
Becquerels, Bq
What does one Becquerel mean?
One decay per second
What are the equivalent SI units for a Becquerel?
s^-1
What is the differential equation for radioactive decay?
dN/dT = - λN
What does dN/dT represent?
The rate of change in number of unstable nuclei remaining
What are differential equations used for?
Describing the rate of change of a quantity
What is the symbol for half life?
T1/2
What is the half life of an isotope?
The average time taken for the number of undecayed atoms in a sample to halve
How is half life measured?
Measuring the time taken for the activity of a sample to halve
What do you have to remember to do when measuring the activity of a radioactive source?
Subtract background radiation from readings
What is the equation for the half life of an isotope?
T1/2 = ln2/λ
What is the equation for the number of unstable nuclei remaining at a given time?
N = N0^-λt
What is the exact solution of the differential equation dN/dT = -λN
N = N0^-λt
What is the definition of capacitance?
The charge stored per volt
What are capacitors?
Things which can store electrical charge
What is the symbol for capacitance?
C
What is the equation for capacitance?
C = Q/V
What are the units of capacitance?
Farads, F
What are the equivalent SI units of a farad?
CV^-1
What is the equation which links current, charge and time?
I = ΔQ/Δt
What are two uses for capacitors?
flash photography and defibrillators
How can the charge on a capacitor be investigated experimentally?
connect a capacitor to a battery, voltmeter, ammeter and variable resistor
Constantly adjust the variable resistor to try and keep the current constant (which will not be possible when it is nearly fully charged)
Record the pd across the voltmeter at regular intervals until it equals the battery pd
Charge stored = current * time
capacitance = Q/V (gradient of Q vs V graph)
How could capacitance be found graphically?
The gradient of a Q vs V graph
What do capacitors store as well as charge?
electrical energy (initially provided by the battery)
What happens when a capacitor discharges?
It is disconnected from the battery and the circuit is closed
Work is done (by converting electrical energy stored by the capacitor) moving charge from one plate to the other until the charge is equal on both plates
there is zero pd across the capacitor and zero current in the circuit
What are the two equations for energy stored on a capacitor?
E = 1/2 QV E = 1/2 CV^2