Calculate The Mass Defect of Cobalt-60 Using The Following Information

Mass defect is a fundamental concept in nuclear physics that describes the difference between the total mass of individual nucleons (protons and neutrons) and the mass of the nucleus they form. This phenomenon is directly related to the binding energy that holds the nucleus together. Calculating mass defect helps scientists understand nuclear stability and the energy released in nuclear reactions.

What is mass defect?

Mass defect occurs when the mass of a nucleus is less than the sum of the masses of its individual protons and neutrons. This mass difference is converted into binding energy according to Einstein's famous equation E=mc². The binding energy is what keeps the nucleus together against the repulsive forces between protons.

The concept of mass defect was first proposed by Einstein and is a key part of nuclear physics. It explains why atomic nuclei are more stable than would be expected based on the sum of their individual nucleon masses. The mass defect is typically measured in atomic mass units (u).

How to calculate mass defect

To calculate mass defect, you need to know the atomic mass of the nucleus and the sum of the masses of its individual nucleons. The formula for mass defect is:

Mass Defect = (Sum of masses of individual nucleons) - (Mass of the nucleus)

Where:

Sum of masses of individual nucleons = (Number of protons × mass of proton) + (Number of neutrons × mass of neutron)
Mass of the nucleus is given by the atomic mass of the element

The result will be in atomic mass units (u). You can then convert this to energy using Einstein's equation if needed.

Example calculation

Let's calculate the mass defect for cobalt-60 (Co-60), which has 27 protons and 33 neutrons.

Given:

Mass of proton = 1.007276 u
Mass of neutron = 1.008665 u
Atomic mass of Co-60 = 59.93382 u

Calculation:

Sum of nucleon masses = (27 × 1.007276) + (33 × 1.008665) = 27.207212 + 33.276795 = 60.483907 u Mass defect = 60.483907 - 59.93382 = 0.550087 u

The mass defect of cobalt-60 is approximately 0.550087 atomic mass units.

FAQ

What units are used for mass defect?

Mass defect is typically measured in atomic mass units (u), which is approximately the mass of a single proton or neutron.

How is mass defect related to binding energy?

Mass defect is directly related to binding energy through Einstein's equation E=mc². The mass defect represents the energy that holds the nucleus together.

Can mass defect be negative?

No, mass defect cannot be negative. It represents the difference between the sum of nucleon masses and the nuclear mass, which is always positive.