Radioactivity

Some isotopes are unstable because of their _____

large size or because they have too many or too few neutrons

Unstable nuclei can emit ____ to become more stable + in what form?

radiation

• Radiation can be in the form of a high energy particle or wave

How does this make it more stable?

• As the radiation moves away from the nucleus, it takes some energy with it

  • This reduces the overall energy of the nucleus

  • This makes the nucleus more stable

What is this called?

radioactive decay

What does random decay mean?

• This means it is not possible to know exactly when a particular nucleus will decay

Radioactive decay is defined as:

The spontaneous disintegration of a nucleus to form a more stable nucleus, resulting in the emission of an alpha, beta or gamma particle

Radioactive decay is a random process, which means that:

• There is an equal probability of any nucleus decaying

• It cannot be known which particular nucleus will decay next

• It cannot be known at what time a particular nucleus will decay

• The rate of decay is unaffected by the surrounding conditions

• It is only possible to estimate the proportion of nuclei decaying in a given time period

Radioactive decay is a spontaneous process, which means that: 

• The decay of nuclei is not affected by the presence of other nuclei in the sample

• External factors such as pressure do not have an effect on the decay

What are alpha particles made up of?

Alpha (α) particles are high energy particles made up of 2 protons and 2 neutrons (the same as a helium nucleus)

alpha particles are usually emitted when __

nuclei that are too large

• Alpha is a ___ penetrating type of radiation

  • Alpha particles have a range of ____

low

a few cm in air

What are beta particles?

Beta (β⁻) particles are high energy electrons emitted from the nucleus

When are beta particles emitted?

• β⁻ particles are emitted by nuclei that have too many neutrons

Beta is a _______ ionising type of radiation

moderately

• This is due to it having a charge of +1e

• This means it is able to do some slight damage to cells (less than alpha but more than gamma)

• Beta is a _______ penetrating type of radiation

  • Beta particles have a range of around __ cm - _ m in air, depending on their energy

moderaletly

20 -3

Beta can be stopped by a ________

few millimetres of aluminium foil

Gamma (γ) rays are ______

high energy electromagnetic waves

They are emitted by ____ that need to lose some energy

nuclei

• Gamma is a ____ penetrating type of radiation

  • Gamma particles have a range of around _ - __cm in lead or several metres in concrete

highly

1-10

• If these particles hit other atoms, they can knock out electrons, ionising the atom

• This can cause chemical changes in materials and can damage or kill living cells

• aim of this experiment is to investigate the penetration powers of different types of radiation using either radioactive sources or simulations

• Independent variable = Absorber material

• Dependent variable = Count rate

• Control variables:

  • Radioactive source

  • Distance of GM tube to source

  • Location / background radiation

1. Connect the Geiger-Müller tube to the counter and, without any sources present, measure background radiation over a one minute period

2. Repeat this three times, and take an average

3. Now place a radioactive source a fixed distance of 3 cm away from the tube and take another reading over a one minute interval

4. Now take a set of absorbers: some paper, several different thicknesses of aluminium (increasing in 0.5mm intervals) and different thickness of lead

5. One at a time, place these absorbers between the source and the tube and take another reading over a one minute interval

6. Repeat the above experiment for other radioactive sources

Results

• Alpha radiation will be absorbed by the paper

• Beta radiation will be absorbed by the aluminium foil

• Some gamma radiation will be absorbed by the thick lead

Safety Considerations

• When not using a source, keep it in a lead lined container

• When in use, try and keep a good distance (a metre or so) between yourself and the source

• When handling the source, do so using tweezers (or tongs) and point the source away from you

Alpha Decay

• During alpha decay an alpha particle is emitted from an unstable nucleus

• A completely new element is formed in the process

Beta Decay

• During beta decay, a neutron changes into a proton and an electron

  • The electron is emitted and the proton remains in the nuclei

• A completely new element is formed because the atomic number changes

The decay constant λ is defined as:

The probability, per second, that a given nucleus will decay

• When a sample is highly radioactive, this means the number of decays per unit time is very high

  • This suggests it has a high level of activity

Activity, or the number of decays per unit time can be calculated using:

A = activity of the sample (Bq)

ΔN = number of decayed nuclei

Δt = time interval (s)

λ = decay constant (s-1)

N = number of nuclei remaining in a sample

The activity of a sample is measured in ________

Becquerels (Bq)

• An activity of 1 Bq is equal to one decay per second, or 1 s^-1

This equation shows:

• The greater the decay constant, the greater the activity of the sample

• The activity depends on the number of undecayed nuclei remaining in the sample

• The minus sign indicates that the number of nuclei remaining decreases with time - however, for calculations it can be omitted

Half life is defined as:

The time taken for the initial number of nuclei to reduce by half

this means when a time equal to the half-life has passed, the activity of the sample will ___ + why?

half

• This is because activity is proportional to the number of undecayed nuclei, A ∝ N

• To find an expression for half-life, start with the equation for exponential decay:

N = N₀e^–λt

• N = number of nuclei remaining in a sample

• N₀ = the initial number of undecayed nuclei (when t = 0)

• λ = decay constant (s^-1)

• t = time interval (s)

• When time t is equal to the half-life t_½, the activity N of the sample will be half of its original value, so N = ½ N₀

what does this show:

This equation shows that half-life t½ and the radioactive decay rate constant λ are inversely proportional

Therefore, the shorter the half-life, the larger the decay constant and the faster the decay

graph of number of undecayed nuclei against time

• The steeper the slope, the larger the decay constant λ (and vice versa)

• The decay curves always start on the y-axis at the initial number of undecayed nuclei (N₀)

The received count rate C is related to the activity of the sample, hence it can also be represented in exponential form by the equation:

C = C₀ e^–λt

• C = count rate at a certain time t (counts per minute or cpm)

• C₀ = initial count rate (counts per minute or cpm)

spreadsheet to model the exponential decay of nuclei:

1. Start with a given number of undecayed nuclei, N₀  in the sample

• N₀  = 1000 is a logical number to start with

       2. Choose a very small interval of time, Δt 

• This should be significantly shorter than the half-life of the isotope chosen

       3. Calculate the number of nuclei decaying, ΔN during the time period

• ∆N∆t = -λN

• So, ΔN = (λΔt) x N

     4. Calculate the number of undecayed nuclei, N now left at the end of the time period, Δt 

• N₀ - ΔN = N

     5. Repeat this process by iterating your value for N as your new N₀  for many values of Δt 

The isotope ______ is commonly used in radioactive dating

carbon-14

how is it formed:

It forms as a result of cosmic rays knocking out neutrons from nuclei, which then collide with nitrogen nuclei in the air:

¹n + ¹⁴N → ¹⁴C + ¹p

How does carbon-14 get it stuff?

• Plants take in carbon dioxide from the atmosphere for photosynthesis, including the radioactive isotope carbon-14

• Animals and humans take in carbon-14 by eating the plants

  • Therefore, all living organisms absorb carbon-14, but after they die they do not absorb any more

is amount constant?

• The proportion of carbon-14 is constant in living organisms as carbon is constantly being replaced during the period they are alive

• When they die, the activity of carbon-14 in the organic matter starts to fall, with a half-life of around __ years

5730

how does it work ?

• Samples of living material can be tested by comparing the current amount of carbon-14 in them and compared to the initial amount (which is based on the current ratio of carbon-14 to carbon-12), and hence they can be dated

problems:

• Carbon dating is a highly reliable ageing method for samples ranging from around 1000 years old up to a limit of around 40 000 years old

  • Therefore, for very young, or very old samples, carbon dating is not the most reliable method to use

This can be explained by looking at the decay curve of carbon-14:

If the sample is less than 1000 years old:

• The activity of the sample will be too high

• So, it is difficult to accurately measure the small change in activity

• Therefore, the ratio of carbon-14 to carbon-12 will be too high to determine an accurate age

If the sample is more than 40 000 years old:

• The activity will be too small and have a count rate similar to that of background radiation

• So, there will be very few carbon-14 atoms remaining, hence very few decays will occur

• Therefore, the ratio of carbon-14 to carbon-12 will be too small to determine an accurate age

other prob:

• Carbon dating uses the currently known ratio of carbon-14 to carbon-12, however, scientists cannot know the level of carbon-14 in the biosphere thousands of years ago

• Therefore, this makes it difficult to age samples which are very old