10: Equations Flashcards

1
Q

Activity = (in terms of N)

A

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

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2
Q

Activity = (in terms of initial activity)

A

A = A₀ e ^ ⁻λt

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3
Q

Discharging capacitor: I =

A

I = I₀ * e⁻ᵗ/ᴿᶜ

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4
Q

Discharging capacitor: V =

A

V = V₀* e⁻ᵗ/ᴿᶜ

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5
Q

Charging capacitor: Q =

A

Q = Q₀* (1 - e⁻ᵗ/ᴿᶜ)

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6
Q

Charging capacitor: V =

A

V = V₀* (1 - e⁻ᵗ/ᴿᶜ)

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7
Q

Charging capacitor: I =

A

I = I₀ * e⁻ᵗ/ᴿᶜ

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8
Q

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

A

lnA = lnA0 -λt

y =mx + c

lnA = y
lnA0 = c
m = -λ
x = t

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9
Q

how to find half life given decay constant

A

T1/2 = ln2 / decay constant

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10
Q

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

A

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

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11
Q

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

A

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

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12
Q

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

A

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

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13
Q

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

A

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

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