Radioactivity and Capacitors

Question 1

Activity, A

Answer 1

Number of nuclei decaying per second

1 Bequerel, Bq = 1 decay per second

Question 2

Half Life, T1/2

Answer 2

The time required for the number of unstable nuclei in a sample to fall by half

Question 3

The random nature of decay

Answer 3

It is random when each individual nucleus will decay, however for different elements and samples the long term trend rate of decay is generally very predictable

Question 4

Decay `Constant

Answer 4

λ = decay constant, probability of a particular nucleus
decaying in one second

A = λN therefore they are directly proportional

A = activity
N = number of nuclei present

Question 5

Rate of decay formula

Answer 5

ΔN = -λNΔt ΔN/Δt = -λN

Exponential decay like this can be modelled iteratively

Question 6

Exponential decay and activity level

Answer 6

N = No.e^-λt

A = Ao.e^-λt

Question 7

Half life formula

Answer 7

T1/2 = ln(2)/λ

Question 8

Capacitors

Answer 8

Metal sheets or plates separated by an insulating layer, that when a p.d. is put across them store charge bc -ve charge is pushed round on to one side, and taken away from the other but is unable to go across it

Question 9

Capacitance

Answer 9

C = Q/V
(farad) = (coulomb)/(volt)

1 Farad is a very large unit so is often used in terms of micro or pico farads

Question 10

Energy stored on a capacitor

Answer 10

E = 1/2 QV
= 1/2 CV^2
= 1/2 Q^2/C

Question 11

Modelling capacitor discharge

Answer 11

ΔQ = -IΔt = -V/RΔt = -Q/RCΔt

ΔQ/Δt = -Q/RC

This process can be solved iteratively

Question 12

Exponential decay formula

Answer 12

Q = Qo.e^-t/RC

V = Vo.e^-t/RC

I = Io.e^-t/RC

Question 13

Time Constant

Answer 13

τ = RC

After RC seconds the charge has been reduced to 1/e of its original value (approx 0.37). This time period is the time constant.

0.693RC = 0.5
RC = 0.37
2RC = 0.14
3RC = 0.05