10: Equations

Question 1

Activity = (in terms of N)

Answer 1

A = λN
A (becquerels, Bq)
λ = Decay constant (s^-1)
N = No. of undecayed nuclei

Question 2

Activity = (in terms of initial activity)

Answer 2

A = A₀ e ^ ⁻λt

Question 3

Discharging capacitor: I =

Answer 3

I = I₀ * e⁻ᵗ/ᴿᶜ

Question 4

Discharging capacitor: V =

Answer 4

V = V₀* e⁻ᵗ/ᴿᶜ

Question 5

Charging capacitor: Q =

Answer 5

Q = Q₀* (1 - e⁻ᵗ/ᴿᶜ)

Question 6

Charging capacitor: V =

Answer 6

V = V₀* (1 - e⁻ᵗ/ᴿᶜ)

Question 7

Charging capacitor: I =

Answer 7

I = I₀ * e⁻ᵗ/ᴿᶜ

Question 8

graphical form of A = A0 e^-λt
what does each part represent

Answer 8

lnA = lnA0 -λt

y =mx + c

lnA = y
lnA0 = c
m = -λ
x = t

Question 9

how to find half life given decay constant

Answer 9

T1/2 = ln2 / decay constant

Question 10

iterative equation for number of nuclei decaying in a time interval
what does the negative sign show
what type of equation is this

Answer 10

ΔN / Δt = -λN
the negative sign shows the number of nuclei decreases after every decay
this is a differential equation

Question 11

what can we see about the relationship between the number of nuclei remaining and activity

Answer 11

the number of nuclei remaining is proportional to the activity
ΔN / Δt ∝ -N

Question 12

how to find the undecayed nuclei N remaining after L half lives

Answer 12

N = 2^L
number of undecayed nuclei remaining = 2^number of half lives

Question 13

how to find change in charge in a set time interval from the differential equation
dQ / dt = -Q / RC

Answer 13

change ds to Δ
ΔQ = -(Q/RC)Δt
so to find changes in Q over a time interval
-original charge / resistance * capacitance) * time interval