Find the binding energy in an atom of ³He, which has a mass of 3.016030 amu.

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Identify the components of the helium-3 nucleus: it contains 2 protons and 1 neutron.

Calculate the mass of the individual nucleons: the mass of a proton is approximately 1.007276 amu and the mass of a neutron is approximately 1.008665 amu.

Determine the total mass of the nucleons if they were separate: add the mass of 2 protons and 1 neutron.

Subtract the actual mass of the helium-3 nucleus (3.016030 amu) from the total mass of the separate nucleons to find the mass defect.

Convert the mass defect from amu to energy using Einstein's equation, \( E = \Delta m \cdot c^2 \), where \( c \) is the speed of light (\( 3.00 \times 10^8 \) m/s).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Binding Energy

Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It reflects the stability of the nucleus; a higher binding energy indicates a more stable nucleus. This energy can be calculated using the mass defect, which is the difference between the mass of the nucleus and the sum of the masses of its individual nucleons.

Mass Defect

The mass defect is the difference between the total mass of the separate nucleons and the mass of the nucleus itself. This discrepancy arises because some mass is converted into energy when nucleons bind together, according to Einstein's equation E=mc². The mass defect is crucial for calculating the binding energy of an atom.

Atomic Mass Unit (amu)

An atomic mass unit (amu) is a standard unit of mass that quantifies mass on an atomic or molecular scale. It is defined as one twelfth of the mass of a carbon-12 atom. In nuclear physics, using amu allows for easier calculations of binding energy and mass defect, as it provides a consistent scale for comparing atomic and subatomic masses.

Find the binding energy in an atom of 3He, which has a mass of 3.016030 amu.