2. Radioactivity Flashcards
What is activity?
A
Activity or number of disintegrations
Number of decays per unit time
Activity is proportional to N which is the number of decaying atoms in a system
Often use seconds as time unit but can use minute hour day
What is the disintegration constant?
λ
Proportional to A
It is the inverse of the mean life (τ)
1/τ = λ
Units are inverse time 1/s
What is specific activity?
The number of decays per unit time per unit mass
What are the equations for activity?
A(t) = Ao • e^(-t/τ)
t is time and τ is mean life
A(t)=Ao • e^(-λt)
A(t)=Ao • e^(-0.693t/T1/2)
A(t)=R • (1-e^-λt)
Where R is rate of production of atoms (when we beam particles at a target material)
A(t)=Rτ • (1-e^-t/τ)
(Page 44)
What are the equations for Number of decays (N)?
N(t) = No • e^(-t/τ)
t is time and τ is mean life
N(t)=No • e^(-λt)
N(t)=No • e^(-0.693t/T1/2)
N(t)=R • (1-e^-λt)
Where R is rate of production of atoms (when we beam particles at a target material)
N(t)=Rτ • (1-e^-t/τ)
(Page 44)
What is the mean life?
How do you convert half life to mean life?
How do you find the decay constant with this?
τ
After one mean life, the number of radioactive atoms and the decay rate would decrease to 1/e or 0.368 or 36.8% of the original intensity
N(τ)/No = A(τ)/Ao = 1/e = 0.368
T1/2 = 0.693τ
1/τ = λ
τ=0.693/λ
What is half life?
What is the half life to mean life conversion?
T1/2
One half life is when 50% of the radioactive atoms decay and the level of radioactivity decreases to half or 50% level of intensity
T1/2=0.693τ
In one half life, A(t=T1/2) = Ao/2
In n half lives, A(t=nT1/2) = Ao(1/2)^n
What is the Curie and Bequerel units?
Curie- 1 Ci is 3.7x10^10 disintegrations per second
Bequerel unit- one decay per second is 1 Bq
What is the relation between activity (A) and number of decays (N)?
A(t) = λN(t)
What are the three types or radiation?
Alpha- positive charge nuclei of helium atoms
Beta- negatively charged particles emitted by atomic nuclei, basically identical to atomic electrons
Gamma- electromagnetic radiation, also emitted by atomic nuclei
Study 4n, 4n+1, 4n+2, and 4n+3 series on pages 34-37
Ok
What is secular equilibrium?
What is transient equilibrium?
Secular- a daughter is in secular equilibrium with its parent if the emissions of the daughter product follow the mean life of the parents
When the parents mean life is much longer than the daughters
Transient- occurs when the mean life of the parent is slightly bigger
When in transient equilibrium,
A(daughter)= A(parent)-T1/2(parent)/T1/2(parent)-T1/2(daughter)
What are the types of decays written with elements for alpha and beta?
Alpha-
(A,Z) X -> (A-4,Z-2) X’ + (4,2) He (alpha particle)
When alpha, mass number drops by 4 and atomic number by 2
Beta-
β-
(A,Z) X -> (A,Z+1) X’ + β- + v (anti neutron)
β+
(A,Z) X -> (A,Z-1) X’ + β+ + ν (neutron)
How do we rearrange activity and number of atoms equations to find time?
t= 1/λ ln[Ao/A(t)] = τln[Ao/A(t)] = T1/2/0.693 ln[Ao/A(t)]
Same for N
Page 47
When a questions asks how long should we irradiate a target to make 99%, 60%, and 20% of saturation activity, what are the steps?
At=Rτ (1-e^-t/τ)
For 99%, At/R = 0.99, t=4.6τ
For 60%, At/R = 0.6, t=0.9τ
For 20%, At/R = 0.2, t=0.22τ
Use this to find the time
