Why is a nucleus lighter than its separate nucleons?

Energy is released when the nucleons bind, and that energy has an equivalent mass (E = mc²), so the nucleus has less mass.

Define binding energy.

The minimum energy needed to separate a nucleus into its individual protons and neutrons.

What is binding energy per nucleon?

The binding energy of the nucleus divided by its nucleon number A.

What is the atomic mass unit u?

One twelfth of the mass of a carbon-12 atom, 1.661 \times 10^{-27} kg.

How do you convert a mass deficit in u to an energy in joules?

Multiply by 1.661 \times 10^{-27} to get kg, then by c^2 = 9.00 \times 10^{16} m² s⁻².

Is mass destroyed when a nucleus forms?

No. Mass and energy are equivalent, and it is the total mass-energy that is conserved.

Should you use atomic or nuclear mass for a mass deficit?

Nuclear mass, so that electron masses are not included in the calculation.

What does a high binding energy per nucleon indicate?

The nucleons are tightly bound, so the nucleus is very stable.

Nuclear binding energyEdexcel A-Level Physics: Flashcards

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What is the mass deficit of a nucleus?

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What is the mass deficit of a nucleus?: The total mass of the separate protons and neutrons minus the mass of the nucleus.
Why is a nucleus lighter than its separate nucleons?: Energy is released when the nucleons bind, and that energy has an equivalent mass (E = mc²), so the nucleus has less mass.
State the equation linking energy and mass deficit.: $E = c^2 \Delta m$
Define binding energy.: The minimum energy needed to separate a nucleus into its individual protons and neutrons.
What is binding energy per nucleon?: The binding energy of the nucleus divided by its nucleon number A.
What is the atomic mass unit u?: One twelfth of the mass of a carbon-12 atom, $1.661 \times 10^{-27}$ kg.
How do you convert a mass deficit in u to an energy in joules?: Multiply by $1.661 \times 10^{-27}$ to get kg, then by $c^2 = 9.00 \times 10^{16}$ m² s⁻².
How many joules are there in 1 MeV?: $1.60 \times 10^{-13}$ J.
Is mass destroyed when a nucleus forms?: No. Mass and energy are equivalent, and it is the total mass-energy that is conserved.
Should you use atomic or nuclear mass for a mass deficit?: Nuclear mass, so that electron masses are not included in the calculation.
What does a high binding energy per nucleon indicate?: The nucleons are tightly bound, so the nucleus is very stable.
Approximately what energy is equivalent to 1 u?: About 931 MeV.

Exam questions on Nuclear binding energy

A student is studying the nucleus of a helium-4 atom, which contains two protons and two neutrons held together by the strong nuclear force. She is comparing the mass of the nucleus with the masses of the particles that it is made from.
Explain why the mass of the helium-4 nucleus is less than the total mass of two separate protons and two separate neutrons.2 marks
The deuteron, the nucleus of hydrogen-2, contains one proton and one neutron. Nuclear mass of the deuteron = 2.013553 u. Mass of a proton = 1.007276 u. Mass of a neutron = 1.008665 u. Take $1\text{ u} = 1.661 \times 10^{-27}$ kg, $c = 3.00 \times 10^{8}$ m s⁻¹ and $e = 1.60 \times 10^{-19}$ C, so that $1\text{ MeV} = 1.60 \times 10^{-13}$ J.
Use your answer to (b) to calculate the binding energy per nucleon of the deuteron, in MeV.2 marks
The Sun transfers energy to space at a rate (power) of $3.8 \times 10^{26}$ W, and this energy comes from nuclear reactions in which mass is converted to energy. The mass of the Sun is $2.0 \times 10^{30}$ kg, its age is $4.6 \times 10^{9}$ years and 1 year = $3.16 \times 10^{7}$ s. Take $c = 3.00 \times 10^{8}$ m s⁻¹ and assume that the power has been constant.
Calculate the mass that the Sun converts to energy each second.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).