10.1 - models, radioactive decay

Question 1

What is a computational model?

Answer 1

A simplified artificial world with objects and rules that you create to model a scenario

Question 2

What does an exponential relationship mean?

Answer 2

The rate of change of a quantity is proportional to the amount of the quantity there is

Question 3

In radioactive decay, what is p?

Answer 3

The probability of a nucleus decaying

Question 4

In radioactive decay, what is N?

Answer 4

The number of non-decayed nuclei left

Question 5

What external conditions can the decay of a nucleus be affected by?

Answer 5

It cannot be affected by any external conditions.

The decay of a nucleus is a quantum event and it cannot be predicted or controlled

Question 6

What is the equation for the probability of a nucleus decaying in a given time period?

Answer 6

p = λΔt

Question 7

What is the symbol for the decay constant?

Answer 7

λ

Question 8

What is the decay constant?

Answer 8

The probability of decay in a fixed time period

Question 9

What is the symbol for activity?

Answer 9

a

lowercase

Question 10

What is activity?

Answer 10

The number of decays happening per second

Question 11

What are the units of activity?

Answer 11

Becquerel, Bq

s^-1

Question 12

What is the equation for activity?

Answer 12

a = λN

Question 13

What is the differential equation used in nuclear decay?

Answer 13

dN/dt = -λN

Question 14

What is the symbol for half life?

Answer 14

t1/2

Question 15

What is the half life?

Answer 15

The time taken for the activity or N to half its original starting value

Question 16

What is the equation for finding the number of non-decayed nuclei at a given time?

Answer 16

N = N0e^-λt

Question 17

What is the equation for finding the activity at a given time?

Answer 17

a = a0e^-λt

Question 18

What is the equation for finding the half life?

Answer 18

t1/2 = ln2/λ

Question 19

What is the equation for finding the decay constant?

Answer 19

λ = p/Δt

Question 20

Using the half life, how can N be calculated for a given time?

Answer 20

N0 x 1/2^x

where x is the number of half lives passed

Question 21

Using the half life, how can a be calculated for a given time?

Answer 21

a0 x 1/2^x

where x is the number of half lives passed

Question 22

If a linear semi-log graph was plotted for nuclear decay, what equation would be used and what would the graph show?

Answer 22

lna = -λt - ln a0
The gradient is the decay constant, λ
The y-intercept is ln of a0

Question 23

What is the equation for the number of non-decayed nuclei left when time passed is the half life?

Answer 23

lnN = lnN0 - ln2

Question 24

How does radiocarbon dating work?

Answer 24

All living things have a constant ratio of carbon-12 to carbon-14 (a radioactive isotope of carbon). When they die, they stop taking in carbon, carbon-14 decays and so the amount of carbon-14 compared to carbon-12 decreases. This decreasing ratio is used to find the time since death.

Question 25

Roughly what is the half life of carbon-14?

Answer 25

5730 years

Question 26

What is the radioactive isotope of carbon?

Answer 26

carbon-14

Question 27

What isotope of carbon is most common?

Answer 27

carbon-12

Question 28

What will happen to the activity if the half life is shorter?

Answer 28

The activity will be greater