Radioactive decay

Question 1

The carbon content of living trees includes a small proportion of C-14, which is a radioactive isotope. After a tree dies, the proportion of C-14 in it decreases due to radioactive decay.
Suggest why the method of carbon dating is likely to be unreliable if a sample is:
a) < 200 years old
b) > 60,000 years old

Answer 1

a) it is difficult to measure the small change in activity accurately.
b) There would be very little to decay

Question 2

State the name of the exchange particle involved in beta+ decay

Answer 2

W+ boson

Question 3

State and explain why environmentalists might have been concerned by the use of such a large quantity of Pu-238

Answer 3

• toxic
• harmful if released into atmosphere
• alphas dangerous when ingested

Question 4

State and explain whether the activity of a given number of atoms of plutonium is affected when they are in form of plutonium oxide

Answer 4

unaffected

chemical bonding involves electrons
radioactivity is nuclear

Question 5

The activity of a radioactive sample =

Answer 5

number of nuclei decaying per second (Bq)

Question 6

unit for activity

Answer 6

Becquerel where 1Bq = 1 decay/second

Question 7

Activity, A =

Answer 7

delta N / delta t = decay constant * number of nuclei = N * -lambda (negative as the number of atoms is decreasing)

Question 8

Activity is proportional to

Answer 8

the number of nuclei therefore amount of activity is proportional to the amount of material present

Question 9

Unit for N

Answer 9

nuclei

Question 10

Decay constant, lambda =

Answer 10

the probability of a nucleus decaying per second
= delta N / delta t * N
= rate of change of N / N

Question 11

A high value of lambda means

Answer 11

a high rate of decay

usually very small (10^-5 sometimes) but can be > 1

Question 12

The number of unstable nuclei remaining, N =

Answer 12

N0 * e^(-lambda * t)

Question 13

The activity of a radioactive sample, A =

Answer 13

A0 * e^(-lambda * t)

Question 14

For a source emitting particles of photons of the same energy, E, the energy transfer per second = the power of the source =

Answer 14

A*E

Question 15

Define half life

Answer 15

the average time taken for the number of nuclei present in an isotope to halve

Question 16

Half life = T1/2 =

Answer 16

ln2 / lambda = 0.69 / lambda

Question 17

To find the half-life from a graph…

Answer 17

use the time it takes for the activity to fall to half the original value i.e. t=0

Question 18

Number of half lives. n =

Answer 18

t / 2*T1/2

Question 19

Remaining number of nuclei after n half lives, N =

Answer 19

N0 * 2^-n

Question 20

The corrected count rate, C is directly proportional to… and so is equal to…

Answer 20

the activity of the source, A

so C= C0 * e^(-lambda * t)

where C0 is the count rate at t=0

Question 21

Mass, M is directly proportional to… so is equal to

Answer 21

the number of nuclei, N

so m = m0 * e^(-lambda*t)

where m0 is the mass at t=0

Question 22

Graph of mass (y axis) against time (x axis)

Answer 22

cuts y axis at m0

tends towards t=0 exponentially

Question 23

Carbon dating:

Answer 23

living plants and trees absorb C-14 and when they die they stop taking it in and so the proportion of C-14 decreases as the nuclei decay. Activity is proportional to the number of atoms still to decay so measuring the activity of the dead sample enables its age to be calculated. Activity falls with half life which can be tested to date them.

Question 24

Argon dating:

Answer 24

rocks contain trapped argon as a result of the decay of radioactive isotope of potassium into argon via electron capture. The age of the rock can be calculated by measuring the proportion of argon gas to potassium

Question 25

Mole =

Answer 25

amount of a substance containing same number of particles (NA = Avagadro’s constant = 6.022x10^23) as there are in 12g of carbon-12

Question 26

1 mole of C-12 has _____ molecules and weights

Answer 26

NA = 6.022x10^23

12g

Question 27

Moles to mass (g) conversion

Answer 27

1 mole = atomic mass (g)

Question 28

Mass (g) to atoms conversion

Answer 28

atomic mass (g) = 6.022x10^23 (NA) particles

Question 29

Moles to atoms conversion

Answer 29

1 mole = 6.022x10^23 (NA) particles

Question 30

When a nucleus emits an alpha or a beta particle it becomes a nucleus of a different _____ because the ______. The number of nuclei of the initial isotope therefore _____ as does the _____ (but just gradually).

Answer 30

element
proton number changes
decreases
mass