calculate δm for the 12c nucleus in units of kg. the mass of a proton is 1.00728 u, and the mass of a neutron is 1.00867 u.

Answers

Answer 1

The mass defect (Δm) of a nucleus is defined as the difference between the mass of its individual nucleons (protons and neutrons) and the actual mass of the nucleus. The mass defect is related to the binding energy of the nucleus by Einstein's famous equation E = mc^2, where c is the speed of light.

The mass of a carbon-12 nucleus (12C) can be calculated as follows:

Number of protons in 12C = 6

Number of neutrons in 12C = 12 - 6 = 6

Mass of 6 protons = 6 x 1.00728 u = 6.04368 u

Mass of 6 neutrons = 6 x 1.00867 u = 6.05202 u

Total mass of 12C = 6.04368 u + 6.05202 u = 12.0957 u

The unified atomic mass unit (u) is defined as 1/12th the mass of a carbon-12 atom, which is 1.66054 x 10^-27 kg. Therefore, the mass of 12C in kilograms can be calculated as:

Mass of 12C = 12.0957 u x (1.66054 x 10^-27 kg/u) = 2.00763 x 10^-26 kg

To calculate the mass defect, we need to compare the mass of the 12C nucleus to the sum of the masses of its individual nucleons. The sum of the masses of 6 protons and 6 neutrons is:

(6 protons x 1.00728 u/proton) + (6 neutrons x 1.00867 u/neutron) = 12.0989 u

Therefore, the mass defect of 12C is:

Δm = (mass of individual nucleons) - (mass of 12C nucleus)

Δm = 12.0989 u - 12.0957 u = 0.0032 u

Finally, we can convert the mass defect to kilograms:

Δm = 0.0032 u x (1.66054 x 10^-27 kg/u) = 5.324 x 10^-30 kg

Therefore, the mass defect of the 12C nucleus is 5.324 x 10^-30 kg.

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Explanation:

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Answers

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