What condition must a nucleus satisfy to be stable, for light isotopes ( Z < 20)?

For light isotopes, stable nuclei follow the line N = Z , meaning equal numbers of neutrons and protons.

How does the stable neutron-to-proton ratio change for heavy isotopes ( Z > 20)?

For heavy isotopes, stable nuclei need more neutrons than protons (N > Z), as the extra neutrons add distance between protons and increase the binding force.

A nucleus will be unstable if it has too many neutrons, too many protons, too many .......... , or too much energy.

A nucleus will be unstable if it has too many neutrons, too many protons, too many nucleons , or too much energy.

Define alpha emission .

Alpha emission occurs in heavy nuclei ( Z > 82) with too many nucleons; emitting an alpha particle (two protons and two neutrons) reduces both the proton number and nucleon number, moving the nucleus closer to the line of stability.

Where on the N-Z graph are beta-minus emitters found, and why?

Beta-minus emitters are found to the left of the stability line, where isotopes are neutron-rich compared to stable isotopes.

Where on the N-Z graph are beta-plus emitters and electron capture found, and why?

Both are found to the right of the stability line, where isotopes are proton-rich compared to stable isotopes.

Define electron capture .

Electron capture occurs when a nucleus captures one of its own orbiting electrons; the electron combines with a proton to form a neutron, releasing a neutrino.

True or False? The strong nuclear force is always attractive, regardless of the separation between nucleons.

False. Below a separation of about 1 fm , the strong nuclear force becomes repulsive , to prevent the nucleus from collapsing.

Define beta-minus (β - ) decay .

In beta-minus decay , a neutron in the nucleus changes into a proton, releasing a β - particle (an electron) and an antineutrino .

How do the neutron number (N) and proton number (Z) change during beta-minus decay?

N decreases by one Z increases by one Nucleon number ( A ) stays constant

Define electron capture .

Electron capture occurs when an orbiting electron is captured by the nucleus and combines with a proton, forming a neutron and releasing a neutrino.

What is the effect on N and Z of beta-plus (β + ) decay or electron capture?

N increases by one Z decreases by one Nucleon number stays constant

Which decay mode occurs when a nucleus has too many nucleons, and how do N and Z change?

Alpha decay occurs; N decreases by two and Z decreases by two (nucleon number decreases by four).

Gamma emission occurs when a nucleus has too much .......... , usually after alpha or beta decay leaves the nucleus in an excited state.

Gamma emission occurs when a nucleus has too much energy , usually after alpha or beta decay leaves the nucleus in an excited state.

True or False? A nucleus with too many protons will decay by alpha emission.

False. A nucleus with too many protons decays by beta-plus emission or electron capture ; alpha emission occurs when there are too many nucleons overall.

Define nuclear excited state .

A nucleus is in an excited state when it holds excess energy above its ground state, in the same way an electron can be excited into a higher energy level.

Does emitting a gamma photon change the number of protons or neutrons in a nucleus?

No — gamma emission does not change the number of protons or neutrons; it only allows the nucleus to lose energy .

Metastable describes a nucleus existing in a particularly stable excited state; the 'm' in technetium-99m denotes this metastable state.

What is technetium-99m used for, and where does it come from?

Technetium-99m is used as a gamma source in medical diagnosis ; it is the decay product of molybdenum-99, which is found in nuclear reactors.

Why is a molybdenum-99 half-life of 66 hours useful for producing technetium-99m for medical use?

A half-life of 66 hours is long enough for the molybdenum-99 sample to be transported to hospitals, where the technetium-99m can then be separated.

Why is a technetium-99m half-life of six hours suitable for medical imaging?

Six hours is an adequate timeframe to examine a patient, but short enough to minimise the damage caused to the patient.

In a nuclear energy level diagram, the decay mode (usually alpha or beta) is represented by a .......... line.

In a nuclear energy level diagram, the decay mode (usually alpha or beta) is represented by a diagonal line.

How are multiple excited states arranged in a nuclear energy level diagram?

Excited states are stacked in descending energy order to the right of the decay line.

True or False? An excited nucleus must always decay directly to its ground state in a single step.

False. An excited nucleus may decay to its ground state either directly or via one or more lower-energy excited states .

Define the closest approach method .

The closest approach method estimates nuclear radius by firing alpha particles at a nucleus and finding the separation at which all their kinetic energy has transferred to electric potential energy.

Why does the closest approach method only give an upper limit (overestimate) for nuclear radius?

It measures the smallest separation between the alpha particle and the nucleus, not the nucleus's actual radius.

Why can the mathematics of the closest approach method not account for high-energy alpha particles that get very close to the nucleus (0.5 to 3 fm)?

Alpha particles contain hadrons, which are affected by the strong nuclear force at this range, and the simple electrostatic maths cannot account for this effect.

Define electron scattering as a method of measuring nuclear radius.

Electron scattering determines nuclear radius by diffracting high-speed electrons around a nucleus and analysing the resulting diffraction pattern.

Give two reasons why electron scattering is more accurate than the closest approach method.

Electron scattering gives a direct measurement of nuclear radius Electrons are leptons , so they are not affected by the strong nuclear force

What feature of the diffraction pattern is used to determine the size of the nucleus in electron scattering?

The size of the nucleus is determined using the angle of the first minimum intensity in the diffraction pattern.

As the speed of an electron increases, its de Broglie wavelength becomes .......... .

As the speed of an electron increases, its de Broglie wavelength becomes smaller .

True or False? Electron diffraction around a nucleus occurs because of the gap between neighbouring nuclei.

False. Electron diffraction occurs because the electron's de Broglie wavelength is comparable to the size of the nucleus itself , not the gap between nuclei.

Define the distance of closest approach .

The distance of closest approach , r , is the separation between an alpha particle and a target nucleus at which all of the alpha particle's initial kinetic energy has been transformed into electric potential energy.

What does Z represent in the closest approach equation?

Z is the proton number of the target nucleus.

The closest approach method gives an .......... limit for the radius of the nucleus, assuming the alpha particle is fired at a high energy.

The closest approach method gives an upper limit for the radius of the nucleus, assuming the alpha particle is fired at a high energy.

True or False? The charge of an alpha particle used in the closest approach calculation is equal to the charge of one proton.

False. An alpha particle has a charge of 2e (twice the charge of a single proton), since it contains two protons.

What is the typical order of magnitude of a nuclear radius?

Nuclear radii are typically of the order 10 -15 m , or 1 fm .

Describe the shape of the graph of nuclear radius R against nucleon number A .

Steep gradient at the origin Gradient gradually decreases to almost horizontal

R 0 is the constant of proportionality in the nuclear radius equation, equal to 1.05 fm .

How can the nuclear radius equation be confirmed graphically using logarithms?

By plotting ln *R against ln A *, which gives a straight line with gradient = 1/3 and y-intercept = ln R 0 .

Plotting a graph of R against A 1/3 gives a straight line through the origin with the gradient equal to .......... .

Plotting a graph of R against A 1/3 gives a straight line through the origin with the gradient equal to R 0 .

True or False? The nucleon number A of a nucleus is directly proportional to its radius R .

False. As nucleons are added the nucleus gets bigger, but A is not proportional to r ; instead R is proportional to A 1/3 .

What is the order of magnitude of nuclear density?

Nuclear density is of the order 10 17 kg m -3 .

What does the constant value of nuclear density show about nucleons in the nucleus?

Nucleons are evenly separated throughout the nucleus, regardless of the size of the nucleus.

Nuclear density is significantly greater than atomic density. What does this suggest?

The majority of the atom's mass is contained in the nucleus The nucleus is very small compared to the atom Atoms must be predominantly empty space

True or False? A nucleus with a larger mass number , A , has a greater nuclear density than a nucleus with a smaller mass number.

False. Nuclear density is constant for all nuclei; the mass number A cancels out of the mass and volume terms, so density does not depend on A or on nuclear radius.

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Nuclear Instability & Radius (AQA A Level Physics): Flashcards

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What condition must a nucleus satisfy to be stable, for light isotopes (Z < 20)?

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What condition must a nucleus satisfy to be stable, for light isotopes (Z < 20)?
For light isotopes, stable nuclei follow the line N = Z, meaning equal numbers of neutrons and protons.
How does the stable neutron-to-proton ratio change for heavy isotopes (Z > 20)?
For heavy isotopes, stable nuclei need more neutrons than protons (N > Z), as the extra neutrons add distance between protons and increase the binding force.
A nucleus will be unstable if it has too many neutrons, too many protons, too many .........., or too much energy.
A nucleus will be unstable if it has too many neutrons, too many protons, too many nucleons, or too much energy.
Define alpha emission.
Alpha emission occurs in heavy nuclei (Z > 82) with too many nucleons; emitting an alpha particle (two protons and two neutrons) reduces both the proton number and nucleon number, moving the nucleus closer to the line of stability.
Where on the N-Z graph are beta-minus emitters found, and why?
Beta-minus emitters are found to the left of the stability line, where isotopes are neutron-rich compared to stable isotopes.
Where on the N-Z graph are beta-plus emitters and electron capture found, and why?
Both are found to the right of the stability line, where isotopes are proton-rich compared to stable isotopes.
Define electron capture.
Electron capture occurs when a nucleus captures one of its own orbiting electrons; the electron combines with a proton to form a neutron, releasing a neutrino.
True or False?
The strong nuclear force is always attractive, regardless of the separation between nucleons.
False.
Below a separation of about 1 fm, the strong nuclear force becomes repulsive, to prevent the nucleus from collapsing.
Define beta-minus (β^-) decay.
In beta-minus decay, a neutron in the nucleus changes into a proton, releasing a β^- particle (an electron) and an antineutrino.
How do the neutron number (N) and proton number (Z) change during beta-minus decay?
- N decreases by one
- Z increases by one
- Nucleon number (A) stays constant
Define electron capture.
Electron capture occurs when an orbiting electron is captured by the nucleus and combines with a proton, forming a neutron and releasing a neutrino.
What is the effect on N and Z of beta-plus (β⁺) decay or electron capture?
- N increases by one
- Z decreases by one
- Nucleon number stays constant
Which decay mode occurs when a nucleus has too many nucleons, and how do N and Z change?
Alpha decay occurs; N decreases by two and Z decreases by two (nucleon number decreases by four).
Gamma emission occurs when a nucleus has too much .........., usually after alpha or beta decay leaves the nucleus in an excited state.
Gamma emission occurs when a nucleus has too much energy, usually after alpha or beta decay leaves the nucleus in an excited state.
True or False?
A nucleus with too many protons will decay by alpha emission.
False.
A nucleus with too many protons decays by beta-plus emission or electron capture; alpha emission occurs when there are too many nucleons overall.
Define nuclear excited state.
A nucleus is in an excited state when it holds excess energy above its ground state, in the same way an electron can be excited into a higher energy level.
Does emitting a gamma photon change the number of protons or neutrons in a nucleus?
No — gamma emission does not change the number of protons or neutrons; it only allows the nucleus to lose energy.
Define metastable.
Metastable describes a nucleus existing in a particularly stable excited state; the 'm' in technetium-99m denotes this metastable state.
What is technetium-99m used for, and where does it come from?
Technetium-99m is used as a gamma source in medical diagnosis; it is the decay product of molybdenum-99, which is found in nuclear reactors.
Why is a molybdenum-99 half-life of 66 hours useful for producing technetium-99m for medical use?
A half-life of 66 hours is long enough for the molybdenum-99 sample to be transported to hospitals, where the technetium-99m can then be separated.
Why is a technetium-99m half-life of six hours suitable for medical imaging?
Six hours is an adequate timeframe to examine a patient, but short enough to minimise the damage caused to the patient.
In a nuclear energy level diagram, the decay mode (usually alpha or beta) is represented by a .......... line.
In a nuclear energy level diagram, the decay mode (usually alpha or beta) is represented by a diagonal line.
How are multiple excited states arranged in a nuclear energy level diagram?
Excited states are stacked in descending energy order to the right of the decay line.
True or False?
An excited nucleus must always decay directly to its ground state in a single step.
False.
An excited nucleus may decay to its ground state either directly or via one or more lower-energy excited states.
Define the closest approach method.
The closest approach method estimates nuclear radius by firing alpha particles at a nucleus and finding the separation at which all their kinetic energy has transferred to electric potential energy.
Write the equation for the distance of closest approach, r, to a gold nucleus.
$r = \frac{158 e^{2}}{4 π ϵ_{0} E_{k}}$
since the charge of an alpha particle is 2e and the charge of a gold nucleus is 79e.
Why does the closest approach method only give an upper limit (overestimate) for nuclear radius?
It measures the smallest separation between the alpha particle and the nucleus, not the nucleus's actual radius.
Why can the mathematics of the closest approach method not account for high-energy alpha particles that get very close to the nucleus (0.5 to 3 fm)?
Alpha particles contain hadrons, which are affected by the strong nuclear force at this range, and the simple electrostatic maths cannot account for this effect.
Define electron scattering as a method of measuring nuclear radius.
Electron scattering determines nuclear radius by diffracting high-speed electrons around a nucleus and analysing the resulting diffraction pattern.
Give two reasons why electron scattering is more accurate than the closest approach method.
- Electron scattering gives a direct measurement of nuclear radius
- Electrons are leptons, so they are not affected by the strong nuclear force
What feature of the diffraction pattern is used to determine the size of the nucleus in electron scattering?
The size of the nucleus is determined using the angle of the first minimum intensity in the diffraction pattern.
As the speed of an electron increases, its de Broglie wavelength becomes ...........
As the speed of an electron increases, its de Broglie wavelength becomes smaller.
True or False?
Electron diffraction around a nucleus occurs because of the gap between neighbouring nuclei.
False.
Electron diffraction occurs because the electron's de Broglie wavelength is comparable to the size of the nucleus itself, not the gap between nuclei.
Write the equation used to accurately determine nuclear radius R from electron diffraction, including the correction factor.
$s i n θ = 1.22 \frac{λ}{2 R}$
where θ is the angle of the first minimum and λ is the de Broglie wavelength.
Define the distance of closest approach.
The distance of closest approach, r, is the separation between an alpha particle and a target nucleus at which all of the alpha particle's initial kinetic energy has been transformed into electric potential energy.
Write the equation for the electric potential energy between an alpha particle and a nucleus of proton number Z, at separation r.
$E_{p} = \frac{2 Z e^{2}}{4 π ϵ_{0} r}$
At the point of closest approach, what is true about the alpha particle's kinetic and potential energy?
All of the alpha particle's initial kinetic energy has been transformed into electric potential energy: $E_{k} = E_{p}$
Write the rearranged equation for the distance of closest approach, r.
$r = \frac{Z e^{2}}{π ϵ_{0} m v^{2}}$
What does Z represent in the closest approach equation?
Z is the proton number of the target nucleus.
The closest approach method gives an .......... limit for the radius of the nucleus, assuming the alpha particle is fired at a high energy.
The closest approach method gives an upper limit for the radius of the nucleus, assuming the alpha particle is fired at a high energy.
True or False?
The charge of an alpha particle used in the closest approach calculation is equal to the charge of one proton.
False.
An alpha particle has a charge of 2e (twice the charge of a single proton), since it contains two protons.
What is the typical order of magnitude of a nuclear radius?
Nuclear radii are typically of the order 10^-15 m, or 1 fm.
Describe the shape of the graph of nuclear radius R against nucleon number A.
- Steep gradient at the origin
- Gradient gradually decreases to almost horizontal
Define R₀.
R₀ is the constant of proportionality in the nuclear radius equation, equal to 1.05 fm.
Write the empirical equation relating nuclear radius R to nucleon number A.
$R = R_{0} A^{1 / 3}$
How can the nuclear radius equation be confirmed graphically using logarithms?
By plotting ln *R against ln A*, which gives a straight line with gradient = 1/3 and y-intercept = ln R₀.
Plotting a graph of R against A^1/3 gives a straight line through the origin with the gradient equal to ...........
Plotting a graph of R against A^1/3 gives a straight line through the origin with the gradient equal to R₀.
True or False?
The nucleon number A of a nucleus is directly proportional to its radius R.
False.
As nucleons are added the nucleus gets bigger, but A is not proportional to r; instead R is proportional to A^1/3.
How is nuclear radius, R, related to mass number, A?
$R = R_{0} A^{1 / 3}$
where $R_{0}$ is a constant of proportionality, equal to 1.05 x 10^-15 m.
How is nuclear mass, m, related to mass number, A?
$m = A u$
where u is the atomic mass unit, equal to 1.661 x 10^-27 kg.
Since volume $V \propto R^{3}$ and $R \propto A^{1 / 3}$ , nuclear volume is proportional to ...........
Since volume $V \propto R^{3}$ and $R \propto A^{1 / 3}$ , nuclear volume is proportional to A.
Define nuclear density.
Nuclear density, $ρ = \frac{m}{V}$ , is constant and independent of nuclear radius, because the mass number A cancels out of the mass and volume terms.
What is the order of magnitude of nuclear density?
Nuclear density is of the order 10¹⁷ kg m^-3.
What does the constant value of nuclear density show about nucleons in the nucleus?
Nucleons are evenly separated throughout the nucleus, regardless of the size of the nucleus.
Nuclear density is significantly greater than atomic density. What does this suggest?
- The majority of the atom's mass is contained in the nucleus
- The nucleus is very small compared to the atom
- Atoms must be predominantly empty space
True or False?
A nucleus with a larger mass number, A, has a greater nuclear density than a nucleus with a smaller mass number.
False.
Nuclear density is constant for all nuclei; the mass number A cancels out of the mass and volume terms, so density does not depend on A or on nuclear radius.

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