Define radioactive decay .

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

Why are some atomic nuclei unstable ?

Because of an imbalance of forces within the nucleus, for example due to a large size or having too many or too few neutrons .

What does it mean for radioactive decay to be a random process?

Every nucleus has an equal probability of decaying, it cannot be known which nucleus will decay next or when , and the rate is unaffected by surrounding conditions.

What does it mean for radioactive decay to be a spontaneous process?

The decay of a nucleus is not affected by the presence of other nuclei in the sample or by external factors such as pressure .

What evidence from a Geiger-Müller tube shows that radioactive decay is random?

The count rate fluctuates irregularly and cannot be predicted, since each count represents the decay of an unstable nucleus.

In the dice-rolling simulation of radioactive decay, each die represents one .......... nucleus in the sample.

In the dice-rolling simulation of radioactive decay, each die represents one undecayed nucleus in the sample.

True or False? Scientists can predict exactly when a particular nucleus will decay.

False. Radioactive decay is a random process, so it is not possible to predict precisely when a particular nucleus will decay.

Define an alpha (α) particle .

An alpha particle is a high energy particle made up of two protons and two neutrons (the same as a helium nucleus), usually emitted from nuclei that are too large.

Define a beta (β⁻) particle .

A beta particle is a high energy electron emitted from the nucleus, by nuclei that have too many neutrons .

Why is gamma (γ) radiation emitted from a nucleus?

Gamma rays are high energy electromagnetic waves emitted by nuclei that need to lose energy .

In the absorption experiment, alpha radiation is absorbed by .......... , while beta radiation is absorbed by aluminium foil.

In the absorption experiment, alpha radiation is absorbed by paper , while beta radiation is absorbed by aluminium foil.

In the radiation absorption experiment, what are the independent and dependent variables?

Independent variable: absorber material. Dependent variable: count rate.

Why is background radiation measured before the absorption experiment begins?

So it can be subtracted from later readings to give the corrected count rate due to the source alone.

True or False? A beta particle has the same magnitude of charge as a proton.

True. A beta particle has a charge of −1*e , the same magnitude as a proton's +1 e * charge, but opposite in sign.

What must be conserved on both sides of a nuclear decay equation?

The sum of the mass numbers and the sum of the atomic numbers before and after the decay.

During alpha decay, the mass number decreases by .......... and the atomic number decreases by two.

During alpha decay, the mass number decreases by four and the atomic number decreases by two.

What happens to a neutron inside the nucleus during beta decay ?

It changes into a proton and an electron ; the electron is emitted and the proton remains in the nucleus.

How do the mass number and atomic number change during beta decay ?

The mass number stays the same ; the atomic number increases by one .

Why does alpha decay always produce a completely new element?

Because the atomic number changes (it decreases by two).

In decay equations, an alpha particle can also be written as a .......... nucleus.

In decay equations, an alpha particle can also be written as a helium nucleus.

A nucleus with 84 protons and 126 neutrons undergoes alpha decay. What are the atomic number and mass number of the new nucleus?

Atomic number = 82 ; mass number = 206 .

True or False? During beta decay, the mass number of the nucleus changes.

False. The mass number stays the same during beta decay, since the emitted electron has negligible mass; only the atomic number changes.

Define the decay constant λ .

The decay constant is the probability, per second, that a given nucleus will decay.

Define the activity of a radioactive sample.

Activity is the number of decays per unit time in a sample, measured in becquerels (Bq) .

One becquerel (Bq) is equal to .......... decay per second.

One becquerel (Bq) is equal to one decay per second.

What effect does a larger decay constant have on a sample's activity?

A larger decay constant means a greater activity , since decay happens faster.

Half-life is the time taken for the initial number of nuclei in a sample to reduce by half.

How are half-life and the decay constant related?

They are inversely proportional : a shorter half-life means a larger decay constant and faster decay.

In the protactinium half-life experiment, what is plotted to find λ from the gradient?

A graph of ln *C (corrected count rate) against time t ; the gradient equals − λ*.

Why is the GM tube positioned close to, but not touching, the bottle in the protactinium experiment?

So that only the beta particles from protactinium are detected, since alpha particles from uranium are absorbed by the bottle.

In the protactinium experiment, shaking the bottle dissolves protactinium into the .......... layer, which then floats to the top.

In the protactinium experiment, shaking the bottle dissolves protactinium into the organic layer, which then floats to the top.

True or False? After two half-lives have passed, the activity of a sample falls to a quarter of its initial value.

True. Each half-life halves the activity, so after two half-lives the activity is half of a half, which is a quarter of the initial value.

On a graph of the number of undecayed nuclei against time, a .......... slope corresponds to a larger decay constant λ .

On a graph of the number of undecayed nuclei against time, a steeper slope corresponds to a larger decay constant λ .

True or False? The number of undecayed nuclei in a radioactive sample eventually reaches zero.

False. Exponential decay means N falls rapidly but never actually reaches zero .

What condition must the time interval, Δt , satisfy in the iterative method for modelling radioactive decay?

Δt must be significantly shorter than the half-life of the isotope being modelled.

At the end of each time interval, the new number of undecayed nuclei is found using N = N₀ − ..........

At the end of each time interval, the new number of undecayed nuclei is found using N = N₀ − ΔN

Why is each newly calculated value of N used as the new N₀ in the next step of the iteration?

The iterative method repeats the same decay calculation over many small time intervals, so the result of one step becomes the starting value for the next.

True or False? When iterating, you should round N to a sensible number of significant figures before using it as N₀ in the next step.

False. The full, unrounded value of N should be kept (e.g. stored in a calculator), since rounding significantly changes the calculated value of N over many iterations.

Why is a spreadsheet a useful tool for modelling radioactive decay?

It allows the iterative decay calculation to be repeated over many small time intervals, producing a table of results and a decay graph.

Define carbon dating .

Carbon dating compares the current amount of carbon-14 in a sample to its initial amount (based on the present-day ratio of carbon-14 to carbon-12) to estimate the sample's age.

Why does the proportion of carbon-14 stay constant in a living organism?

Living organisms continually absorb carbon-14 (plants via photosynthesis, animals and humans by eating plants), so it is constantly replaced.

After an organism dies, it stops absorbing carbon-14 and its activity begins to ..........

After an organism dies, it stops absorbing carbon-14 and its activity begins to fall

Over what age range is carbon dating considered highly reliable?

From around 1000 years to around 40 000 years old.

Why is carbon dating unreliable for samples younger than 1000 years old, or older than 40 000 years old?

Too young: activity is too high, so the small change is hard to measure accurately, giving a ratio too high to date the sample. Too old: activity is too low, similar to background radiation, so very few decays occur, giving a ratio too small to date the sample accurately.

True or False? Carbon dating calculations use the ratio of carbon-14 to carbon-12 that existed in the atmosphere thousands of years ago.

False. Carbon dating uses the current ratio of carbon-14 to carbon-12, since scientists cannot know the exact level of carbon-14 in the biosphere thousands of years ago — this adds uncertainty when dating very old samples.

A LevelPhysicsOCRFlashcards6. Particles & Medical PhysicsRadioactivity

Radioactivity (OCR A Level Physics): Flashcards

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Cards in this collection (56)

Define radioactive decay.
Radioactive decay is the spontaneous disintegration of a nucleus to form a more stable nucleus, resulting in the emission of an alpha, beta or gamma particle.
Why are some atomic nuclei unstable?
Because of an imbalance of forces within the nucleus, for example due to a large size or having too many or too few neutrons.
What does it mean for radioactive decay to be a random process?
Every nucleus has an equal probability of decaying, it cannot be known which nucleus will decay next or when, and the rate is unaffected by surrounding conditions.
What does it mean for radioactive decay to be a spontaneous process?
The decay of a nucleus is not affected by the presence of other nuclei in the sample or by external factors such as pressure.
What evidence from a Geiger-Müller tube shows that radioactive decay is random?
The count rate fluctuates irregularly and cannot be predicted, since each count represents the decay of an unstable nucleus.
In the dice-rolling simulation of radioactive decay, each die represents one .......... nucleus in the sample.
In the dice-rolling simulation of radioactive decay, each die represents one undecayed nucleus in the sample.
True or False?
Scientists can predict exactly when a particular nucleus will decay.
False.
Radioactive decay is a random process, so it is not possible to predict precisely when a particular nucleus will decay.
Define an alpha (α) particle.
An alpha particle is a high energy particle made up of two protons and two neutrons (the same as a helium nucleus), usually emitted from nuclei that are too large.
Define a beta (β⁻) particle.
A beta particle is a high energy electron emitted from the nucleus, by nuclei that have too many neutrons.
Why is gamma (γ) radiation emitted from a nucleus?
Gamma rays are high energy electromagnetic waves emitted by nuclei that need to lose energy.
In the absorption experiment, alpha radiation is absorbed by .........., while beta radiation is absorbed by aluminium foil.
In the absorption experiment, alpha radiation is absorbed by paper, while beta radiation is absorbed by aluminium foil.
In the radiation absorption experiment, what are the independent and dependent variables?
Independent variable: absorber material.
Dependent variable: count rate.
Why is background radiation measured before the absorption experiment begins?
So it can be subtracted from later readings to give the corrected count rate due to the source alone.
True or False?
A beta particle has the same magnitude of charge as a proton.
True.
A beta particle has a charge of −1*e, the same magnitude as a proton's +1e* charge, but opposite in sign.
What must be conserved on both sides of a nuclear decay equation?
The sum of the mass numbers and the sum of the atomic numbers before and after the decay.
During alpha decay, the mass number decreases by .......... and the atomic number decreases by two.
During alpha decay, the mass number decreases by four and the atomic number decreases by two.
What happens to a neutron inside the nucleus during beta decay?
It changes into a proton and an electron; the electron is emitted and the proton remains in the nucleus.
How do the mass number and atomic number change during beta decay?
The mass number stays the same; the atomic number increases by one.
Why does alpha decay always produce a completely new element?
Because the atomic number changes (it decreases by two).
In decay equations, an alpha particle can also be written as a .......... nucleus.
In decay equations, an alpha particle can also be written as a helium nucleus.
A nucleus with 84 protons and 126 neutrons undergoes alpha decay. What are the atomic number and mass number of the new nucleus?
Atomic number = 82; mass number = 206.
True or False?
During beta decay, the mass number of the nucleus changes.
False.
The mass number stays the same during beta decay, since the emitted electron has negligible mass; only the atomic number changes.
Define the decay constant λ.
The decay constant is the probability, per second, that a given nucleus will decay.
Define the activity of a radioactive sample.
Activity is the number of decays per unit time in a sample, measured in becquerels (Bq).
One becquerel (Bq) is equal to .......... decay per second.
One becquerel (Bq) is equal to one decay per second.
Write the equation linking activity A, the decay constant λ, and the number of undecayed nuclei N.
$A = λ N$
What effect does a larger decay constant have on a sample's activity?
A larger decay constant means a greater activity, since decay happens faster.
True or False?
The activity of a sample is independent of the number of undecayed nuclei remaining.
False.
Activity depends on the number of undecayed nuclei, since $A = λ N$ ; activity falls as N decreases.
Define half-life.
Half-life is the time taken for the initial number of nuclei in a sample to reduce by half.
Write the equation relating half-life t_1/2 to the decay constant λ.
$t_{1 / 2} = \frac{\ln 2}{λ}$
How are half-life and the decay constant related?
They are inversely proportional: a shorter half-life means a larger decay constant and faster decay.
In the protactinium half-life experiment, what is plotted to find λ from the gradient?
A graph of ln *C (corrected count rate) against time t; the gradient equals −λ*.
Why is the GM tube positioned close to, but not touching, the bottle in the protactinium experiment?
So that only the beta particles from protactinium are detected, since alpha particles from uranium are absorbed by the bottle.
In the protactinium experiment, shaking the bottle dissolves protactinium into the .......... layer, which then floats to the top.
In the protactinium experiment, shaking the bottle dissolves protactinium into the organic layer, which then floats to the top.
True or False?
After two half-lives have passed, the activity of a sample falls to a quarter of its initial value.
True.
Each half-life halves the activity, so after two half-lives the activity is half of a half, which is a quarter of the initial value.
Write the exponential decay equation for the number of undecayed nuclei N remaining after time t.
$N = N_{0} e^{- λ t}$
Write the equivalent exponential decay equation for the activity A of a sample.
$A = A_{0} e^{- λ t}$
On a graph of the number of undecayed nuclei against time, a .......... slope corresponds to a larger decay constant λ.
On a graph of the number of undecayed nuclei against time, a steeper slope corresponds to a larger decay constant λ.
What is the inverse function of e^x, and what is it called?
$\ln y$ , the natural logarithmic function; if $e^{x} = y$ , then $x = \ln y$ .
Define N₀ in the equation $N = N_{0} e^{- λ t}$ .
N₀ is the initial number of undecayed nuclei in the sample, at t = 0.
True or False?
The number of undecayed nuclei in a radioactive sample eventually reaches zero.
False.
Exponential decay means N falls rapidly but never actually reaches zero.
Define activity.
Activity, A, is the number of nuclei that decay per unit time, measured in becquerels (Bq):
$A = \frac{Δ N}{Δ t} = - λ N$
What condition must the time interval, Δt, satisfy in the iterative method for modelling radioactive decay?
Δt must be significantly shorter than the half-life of the isotope being modelled.
How is the number of nuclei decaying in a time interval, ΔN, calculated in the iterative method?
$Δ N = (λ Δ t) \times N$
using the current value of N.
At the end of each time interval, the new number of undecayed nuclei is found using N = N₀ − ..........
At the end of each time interval, the new number of undecayed nuclei is found using N = N₀ − ΔN
Why is each newly calculated value of N used as the new N₀ in the next step of the iteration?
The iterative method repeats the same decay calculation over many small time intervals, so the result of one step becomes the starting value for the next.
True or False?
When iterating, you should round N to a sensible number of significant figures before using it as N₀ in the next step.
False.
The full, unrounded value of N should be kept (e.g. stored in a calculator), since rounding significantly changes the calculated value of N over many iterations.
Why is a spreadsheet a useful tool for modelling radioactive decay?
It allows the iterative decay calculation to be repeated over many small time intervals, producing a table of results and a decay graph.
Define carbon dating.
Carbon dating compares the current amount of carbon-14 in a sample to its initial amount (based on the present-day ratio of carbon-14 to carbon-12) to estimate the sample's age.
How is carbon-14 produced in the atmosphere?
Cosmic rays knock neutrons out of nuclei; these neutrons collide with nitrogen-14 nuclei to produce carbon-14 and a proton:
${}^{1}n +^{14} N \to^{14} C +^{1} p$
Why does the proportion of carbon-14 stay constant in a living organism?
Living organisms continually absorb carbon-14 (plants via photosynthesis, animals and humans by eating plants), so it is constantly replaced.
After an organism dies, it stops absorbing carbon-14 and its activity begins to ..........
After an organism dies, it stops absorbing carbon-14 and its activity begins to fall
What is the half-life of carbon-14?
Around 5730 years.
Over what age range is carbon dating considered highly reliable?
From around 1000 years to around 40 000 years old.
Why is carbon dating unreliable for samples younger than 1000 years old, or older than 40 000 years old?
Too young: activity is too high, so the small change is hard to measure accurately, giving a ratio too high to date the sample.
Too old: activity is too low, similar to background radiation, so very few decays occur, giving a ratio too small to date the sample accurately.
True or False?
Carbon dating calculations use the ratio of carbon-14 to carbon-12 that existed in the atmosphere thousands of years ago.
False.
Carbon dating uses the current ratio of carbon-14 to carbon-12, since scientists cannot know the exact level of carbon-14 in the biosphere thousands of years ago — this adds uncertainty when dating very old samples.

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