IB Physics Topic E.3.1 Stability and Binding Energy Revision Notes (SL/HL)

IB Physics Topic E.3.1 Stability and Binding Energy Revision Notes (SL/HL) | RevisionDojo

Written by official IB examiners

Understanding Isotopes, Nuclear Stability, and the Strong Nuclear Force

Every atom is defined by its number of protons, denoted as $Z$, which determines the element.
However, not all carbon atoms are identical. They can have different numbers of neutrons, $N$.
The total number of protons and neutrons, called the nucleon number, is denoted as $A$, where: $$
A = Z + N
$$
Atoms of the same element with different numbers of neutrons are called isotopes.

Example

Carbon-12 ($^{12}_6 \text{C}$): 6 protons and 6 neutrons.
Carbon-14 ($^{14}_6 \text{C}$): 6 protons and 8 neutrons.

Key Properties of Isotopes

Same chemical properties: chemical behaviour depends on the number of electrons, and isotopes of an element have the same $Z$, so they react in the same way.
Different physical properties: The difference in neutron number affects properties like mass and nuclear stability.

Example

Consider the isotope $^{23}_{11} \text{Na}$.
- Proton number ($Z$) = 11
- Nucleon number ($A$) = 23
- Neutron number ($N$) = $A - Z = 23 - 11 = 12$
This sodium isotope has 12 neutrons.

Note

The existence of isotopes is direct evidence for the presence of neutrons in the nucleus, as $A$ can vary while $Z$ remains fixed.

Active recall

How would you calculate the number of neutrons in the isotope $^{16}_8 \text{O}$?

Binding Energy Per Nucleon: A Measure of Stability

When you assemble protons and neutrons to form a nucleus, the total mass of the nucleus is slightly less than the sum of the individual masses of its protons and neutrons.

This "missing mass" is called the mass defect, and it is converted into energy according to Einstein’s famous equation: $$
E = mc^2
$$

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Understanding Isotopes, Nuclear Stability, and the Strong Nuclear Force

Every atom is defined by its number of protons, denoted as $Z$, which determines the element.
However, not all carbon atoms are identical. They can have different numbers of neutrons, $N$.
The total number of protons and neutrons, called the nucleon number, is denoted as $A$, where: $$
A = Z + N
$$
Atoms of the same element with different numbers of neutrons are called isotopes.

Example

Carbon-12 ($^{12}_6 \text{C}$): 6 protons and 6 neutrons.
Carbon-14 ($^{14}_6 \text{C}$): 6 protons and 8 neutrons.

Key Properties of Isotopes

Same chemical properties: chemical behaviour depends on the number of electrons, and isotopes of an element have the same $Z$, so they react in the same way.
Different physical properties: The difference in neutron number affects properties like mass and nuclear stability.

Example

Consider the isotope $^{23}_{11} \text{Na}$.
- Proton number ($Z$) = 11
- Nucleon number ($A$) = 23
- Neutron number ($N$) = $A - Z = 23 - 11 = 12$
This sodium isotope has 12 neutrons.

Note

The existence of isotopes is direct evidence for the presence of neutrons in the nucleus, as $A$ can vary while $Z$ remains fixed.

Active recall

How would you calculate the number of neutrons in the isotope $^{16}_8 \text{O}$?

Binding Energy Per Nucleon: A Measure of Stability

When you assemble protons and neutrons to form a nucleus, the total mass of the nucleus is slightly less than the sum of the individual masses of its protons and neutrons.

This "missing mass" is called the mass defect, and it is converted into energy according to Einstein’s famous equation: $$
E = mc^2
$$

Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

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Duis aute irure dolor in reprehenderit

Note

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Excepteur sint occaecat cupidatat non proident

Tip

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Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

IB Physics E.3.1 Stability and Binding Energy Notes

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

Understanding Isotopes, Nuclear Stability, and the Strong Nuclear Force

Key Properties of Isotopes

Binding Energy Per Nucleon: A Measure of Stability

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Duis aute irure dolor in reprehenderit

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Understanding Isotopes, Nuclear Stability, and the Strong Nuclear Force

Key Properties of Isotopes

Binding Energy Per Nucleon: A Measure of Stability

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Duis aute irure dolor in reprehenderit

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