20.1.3 Binding Energy

Question 1

Binding Energy

Answer 1

• In nuclear reactions, matter is converted into energy.
• Binding energy (E b ) is the energy required to break a nucleus apart into protons and neutrons.
• Higher values of binding energy per nucleon indicate more stable nuclei.

Question 2

note

Answer 2

• In beta decay, a neutron is converted to a proton, emitting a beta particle. The total mass of the products (a proton and an electron) is 1.4 x 10 –30 kg less than the mass of the reactant (a neutron).
• The missing mass was converted to energy. The amount of energy can be found by using Einstein’s theory of relativity, which states that energy (E) is equal to mass (m) times the speed of light squared (c 2 ). In this case, the change in energy (ΔE) is equal to the change in mass (Δm) times the speed of light squared (c 2 ). This calculation works out to –1.3 x 10 –13 J/neutron, or –75 x 10 6 kJ/mol of neutrons—a huge amount of energy. In comparison, for the combustion of carbon to yield carbon dioxide, ΔH = –400 kJ/mol of carbon (about 200,000 times less).
• Binding energy (E b ) is the energy required to break a nucleus apart into protons and neutrons. Binding energy is the opposite of the amount of energy released when the nucleus is formed from nucleons (E b = –ΔE).
• For example, ΔE for the creation of a deuterium ( 2 H) nucleus from a proton and a neutron is –2.15 x 10 8 kJ/mol. Therefore, the binding energy of a deuterium nucleus is 2.15 x 10 8 kJ/mol.
• Dividing the binding energy (E b ) by the number of nucleons in a nucleus yields the binding energy per nucleon. Higher values of binding energy per nucleon indicate more stable nuclei.
• Binding energy per nucleon peaks around iron-56 ( 56 Fe). This means that all nuclei are thermodynamically unstable compared to iron-56.
• Nuclei to the left of iron-56 can undergo nuclear fusion (joining of light nuclei) to form heavier nuclei. Nuclei to the right of iron-56 can undergo nuclear fission (splitting of heavy nuclei) to form lighter nuclei.

Question 3

Which statement about binding energy per nucleon is not correct?

Answer 3

Nuclear fusion reactors are used more frequently to produce energy than nuclear fission reactors. This is because the reactants (hydrogen nuclei) are much more abundant and the products (helium and other light nuclei) are far better for the environment.

Question 4

Which statement about the following reaction is not correct?
1 1 H = 1 0 n -> 2 1 H
Eb = 2.15*10^8 kJ/mol. The mass of 1 1 H is 1.00782 AMU. The mass of 1 0 n is 1.00866 AMU. The mass of 2 1 H is 2.01410 AMU

Answer 4

Δm = 0.00238 AMU

Question 5

Which statement about nuclear particles is not true?

Answer 5

ΔE = mc2, c = 2.9979 × 108 ms−1

Question 6

Which statement about he following reaction, in which an atom of 20 10 Ne is formed, is not correct?
10 1 1 p + 10 1 0 n = 10 0 -1 e -> 20 10 Ne
Remember that for the expression ΔE = mc^2, c = 2.9979 * 10^8 ms-1. Also, the mass of 20 10 Ne is 19.9924 AMU and 1 AMU = 1.6605492 * 10^-27 kg

Answer 6

ΔE is the amount of energy associated with 1 mole of 20 10 Ne

Question 7

Which statement about the following particle reaction is not correct?
1 0 n -> 1 1 p + 0 -1 e

Answer 7

The amount of energy change for a chemical reaction is similar to the amount of energy change for a nuclear reaction.

Question 8

Which statement about binding energy is not correct?

Answer 8

For the reaction 1 1 H + 1 0 n -> 2 1 H the binding energy is the energy needed to make the nucleons join and form 2 1 H

Question 9

Look at the nuclear reaction in which a neutron forms a proton and an electron
1 0 n -> 1 1 p + 0 -1 e
Which statement about this reaction is not correct?

Answer 9

The values for Δm and ΔE are extremely large and significant for the decay of a single neutron.

Question 10

Which statement about ΔE is not correct?

Answer 10

In the reaction 1 0 n -> 1 0 p + 0 -1 e the neutron on the left side of the reaction is at a lower potential energy level than the components on the right side of the reaction

Question 11

Which statement about binding energy is not correct?

Answer 11

ΔE=Eb

Question 12

The following reaction shows how one atom of 20 10 Ne is formed from protons, neutrons, and electrons. What is the value for Δm for this reaction?
10 1 1 p + 10 1 0 n + 10 0 -1 e -> 20 10 Ne
The mass of an electron is 0.00055 AMU
The mass of a proton is 1.00728 AMU
The mass of a neutron is 1.00866 AMU
The mass of 20 10 Ne is 19.9924 AMU

Answer 12

−0.1725 AMU