# 10: Equations Flashcards

Activity = (in terms of N)

A = λN

A (becquerels, Bq)

λ = Decay constant (s^-1)

N = No. of undecayed nuclei

Activity = (in terms of initial activity)

A = A₀ e ^ ⁻λt

Discharging capacitor: I =

I = I₀ * e⁻ᵗ/ᴿᶜ

Discharging capacitor: V =

V = V₀* e⁻ᵗ/ᴿᶜ

Charging capacitor: Q =

Q = Q₀* (1 - e⁻ᵗ/ᴿᶜ)

Charging capacitor: V =

V = V₀* (1 - e⁻ᵗ/ᴿᶜ)

Charging capacitor: I =

I = I₀ * e⁻ᵗ/ᴿᶜ

graphical form of A = A0 e^-λt

what does each part represent

lnA = lnA0 -λt

y =mx + c

lnA = y lnA0 = c m = -λ x = t

how to find half life given decay constant

T1/2 = ln2 / decay constant

iterative equation for number of nuclei decaying in a time interval

what does the negative sign show

what type of equation is this

ΔN / Δt = -λN

the negative sign shows the number of nuclei decreases after every decay

this is a differential equation

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

the number of nuclei remaining is proportional to the activity

ΔN / Δt ∝ -N

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

N = 2^L

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

how to find change in charge in a set time interval from the differential equation

dQ / dt = -Q / RC

change ds to Δ

ΔQ = -(Q/RC)Δt

so to find changes in Q over a time interval

-original charge / resistance * capacitance) * time interval