The difference between the measured mass of a nucleus and the sum total of the masses of its constituents Also known as the mass deficit

Define binding energy

The energy required to break a nucleus into its constituent protons and neutrons

The total mass of a nucleus is .......... than the sum of the masses of its constituent nucleons

The total mass of a nucleus is less than the sum of the masses of its constituent nucleons

True or False? Binding energy is the energy stored inside the nucleus

False. Binding energy is the energy that must be put into a nucleus to pull it apart into its constituent nucleons — it is not energy stored within the nucleus

Give some examples of mass-energy equivalence in physics

Fusion of hydrogen into helium in the Sun Fission of uranium in nuclear power plants Nuclear weapons High-energy particle collisions in particle accelerators

Is the formation of a nucleus from isolated nucleons exothermic or endothermic?

Exothermic — energy is released when a nucleus forms from isolated protons and neutrons, because the bound system has less mass, and therefore less energy, than its separated constituents

Define the unified atomic mass unit (u)

The mass of exactly one-twelfth of an atom of carbon-12 Roughly equal to the mass of one proton or neutron

The atomic mass unit is defined as the mass of exactly .......... of an atom of ..........

The atomic mass unit is defined as the mass of exactly one-twelfth of an atom of carbon-12

What is the mass of one atom of carbon-12 in atomic mass units?

Exactly 12 u This follows directly from the definition of the atomic mass unit as one-twelfth of a carbon-12 atom

The mass of an atom in u is roughly equal to its nucleon number. Why is the actual mass slightly lower than this?

Because of mass-energy equivalence — some mass is released as energy (the mass defect) when the nucleus forms, so the measured mass is slightly less than the sum of the individual nucleon masses

True or False? The mass of an atom in u is exactly equal to its nucleon number

False. The mass in u is only roughly equal to the nucleon number. For example, uranium-235 has a mass of about 235 u, but the actual value is slightly lower because some mass is released as energy when the nucleus forms

Define binding energy per nucleon

The binding energy of a nucleus divided by the number of nucleons in the nucleus

What does a higher binding energy per nucleon indicate?

A higher stability , since more energy is required to pull the nucleus apart

Which element has the highest binding energy per nucleon?

Iron (A = 56) — this makes it the most stable of all the elements and marks the peak of the binding energy per nucleon graph

Nuclei with a low nucleon number are most likely to undergo .......... , while the heaviest nuclei are most likely to undergo ..........

Nuclei with a low nucleon number are most likely to undergo fusion , while the heaviest nuclei are most likely to undergo fission

Which three light nuclei do not fit the general trend on the binding energy per nucleon graph?

Helium-4 , carbon-12 and oxygen-16 Helium-4 is particularly stable, giving it a high binding energy per nucleon Carbon-12 and oxygen-16 behave like three and four helium nuclei bound together

True or False? The heaviest elements have the highest binding energy per nucleon

False. Binding energy per nucleon peaks at iron (A = 56) and then gradually decreases as A increases. The heaviest elements are therefore less stable and likely to undergo fission

Define nuclear fusion

Small nuclides that combine together to make larger nuclei, releasing energy

Which type of nuclei can undergo fusion and release energy?

Low mass nuclei , such as hydrogen and helium

Fusion can only be achieved in an extremely .......... and .......... environment, such as the core of a star

Fusion can only be achieved in an extremely hot and dense environment, such as the core of a star

Why must the two nuclei in a fusion reaction have very high kinetic energy?

To overcome the electrostatic repulsion between their positively charged protons, so they can get close enough for the strong nuclear force to bind them together

Why must fusing nuclei get extremely close together?

The strong nuclear force that binds nucleons acts only over very short distances, so nuclei must get very close before it can take effect

True or False? The nucleus produced by a fusion reaction has the same mass as the nuclei that fused to form it

False. The new, heavier nucleus has less mass than the nuclei that fused. The missing mass is converted into energy, which is why fusion releases energy and the binding energy per nucleon increases

A LevelPhysicsEdexcelFlashcards11. Nuclear RadiationNuclear Fusion & Fission

Nuclear Fusion & Fission (Edexcel A Level Physics): Flashcards

Exam code: 9PH0

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FrontNuclear Binding Energy & Mass Deficit
Define mass defect

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Cards in this collection (30)

Define mass defect
The difference between the measured mass of a nucleus and the sum total of the masses of its constituents
Also known as the mass deficit
Define binding energy
The energy required to break a nucleus into its constituent protons and neutrons
The total mass of a nucleus is .......... than the sum of the masses of its constituent nucleons
The total mass of a nucleus is less than the sum of the masses of its constituent nucleons
State the equation for the mass defect Δm of a nucleus and define each term
$Δ m = Z m_{p} + (A - Z) m_{n} - m_{t o t a l}$
- Z = proton number
- A = nucleon number
- m_p = mass of a proton
- m_n = mass of a neutron
- m_total = measured mass of the nucleus
True or False?
Binding energy is the energy stored inside the nucleus
False.
Binding energy is the energy that must be put into a nucleus to pull it apart into its constituent nucleons — it is not energy stored within the nucleus
What does the equation $Δ E = Δ m c^{2}$ describe?
Mass-energy equivalence — mass can be converted into energy and energy into mass
- E = energy (J)
- m = mass (kg)
- c = speed of light (m s^-1)
Give some examples of mass-energy equivalence in physics
- Fusion of hydrogen into helium in the Sun
- Fission of uranium in nuclear power plants
- Nuclear weapons
- High-energy particle collisions in particle accelerators
Is the formation of a nucleus from isolated nucleons exothermic or endothermic?
Exothermic — energy is released when a nucleus forms from isolated protons and neutrons, because the bound system has less mass, and therefore less energy, than its separated constituents
Define the unified atomic mass unit (u)
The mass of exactly one-twelfth of an atom of carbon-12
Roughly equal to the mass of one proton or neutron
The atomic mass unit is defined as the mass of exactly .......... of an atom of ..........
The atomic mass unit is defined as the mass of exactly one-twelfth of an atom of carbon-12
What is the value of 1 u in kilograms?
$1 u = 1.66 \times 10^{- 27} kg$
This value is provided on the exam data sheet
What is 1 u equivalent to in MeV?
1 u is equivalent to 931.5 MeV
Mass can be expressed as an energy because the two are equivalent via $Δ E = Δ m c^{2}$
What is the mass of one atom of carbon-12 in atomic mass units?
Exactly 12 u
This follows directly from the definition of the atomic mass unit as one-twelfth of a carbon-12 atom
The mass of an atom in u is roughly equal to its nucleon number. Why is the actual mass slightly lower than this?
Because of mass-energy equivalence — some mass is released as energy (the mass defect) when the nucleus forms, so the measured mass is slightly less than the sum of the individual nucleon masses
True or False?
The mass of an atom in u is exactly equal to its nucleon number
False.
The mass in u is only roughly equal to the nucleon number. For example, uranium-235 has a mass of about 235 u, but the actual value is slightly lower because some mass is released as energy when the nucleus forms
Define binding energy per nucleon
The binding energy of a nucleus divided by the number of nucleons in the nucleus
What does a higher binding energy per nucleon indicate?
A higher stability, since more energy is required to pull the nucleus apart
Which element has the highest binding energy per nucleon?
Iron (A = 56) — this makes it the most stable of all the elements and marks the peak of the binding energy per nucleon graph
Nuclei with a low nucleon number are most likely to undergo .........., while the heaviest nuclei are most likely to undergo ..........
Nuclei with a low nucleon number are most likely to undergo fusion, while the heaviest nuclei are most likely to undergo fission
Which three light nuclei do not fit the general trend on the binding energy per nucleon graph?
Helium-4, carbon-12 and oxygen-16
- Helium-4 is particularly stable, giving it a high binding energy per nucleon
- Carbon-12 and oxygen-16 behave like three and four helium nuclei bound together
True or False?
The heaviest elements have the highest binding energy per nucleon
False.
Binding energy per nucleon peaks at iron (A = 56) and then gradually decreases as A increases. The heaviest elements are therefore less stable and likely to undergo fission
Approximately what is the binding energy per nucleon of iron-56, and how is it found?
About 8.7 MeV
Found by calculating the mass defect, converting it to binding energy using $Δ E = Δ m c^{2}$ , dividing by the nucleon number (56), then converting from joules to MeV
Define nuclear fusion
Small nuclides that combine together to make larger nuclei, releasing energy
Which type of nuclei can undergo fusion and release energy?
Low mass nuclei, such as hydrogen and helium
Write the equation for the deuterium-tritium (D-T) fusion reaction
$_1^{2} H +_1^{3} H \to_2^{4} H e +_0^{1} n$
A deuterium and a tritium nucleus fuse to produce a helium nucleus and a neutron
Fusion can only be achieved in an extremely .......... and .......... environment, such as the core of a star
Fusion can only be achieved in an extremely hot and dense environment, such as the core of a star
Why must the two nuclei in a fusion reaction have very high kinetic energy?
To overcome the electrostatic repulsion between their positively charged protons, so they can get close enough for the strong nuclear force to bind them together
Why must fusing nuclei get extremely close together?
The strong nuclear force that binds nucleons acts only over very short distances, so nuclei must get very close before it can take effect
True or False?
The nucleus produced by a fusion reaction has the same mass as the nuclei that fused to form it
False.
The new, heavier nucleus has less mass than the nuclei that fused. The missing mass is converted into energy, which is why fusion releases energy and the binding energy per nucleon increases
In the proton-proton chain, how many hydrogen nuclei fuse to form one helium nucleus?
Four hydrogen nuclei ( $_1^{1} H$ ) fuse to produce one helium nucleus ( $_2^{4} H e$ ), releasing energy that fuels the star

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