How much energy must be supplied to break a single ²¹Ne nucleus into separated protons and neutrons if the nucleus has a mass of 20.98846 amu? What is the nuclear binding energy for 1 mol of ²¹Ne?

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

검증된 단계별 안내

Step 1: Determine the number of protons and neutrons in the ²¹Ne nucleus. Neon (Ne) has an atomic number of 10, which means it has 10 protons. Since the mass number is 21, the number of neutrons is 21 - 10 = 11.

Step 2: Calculate the total mass of the separated protons and neutrons. Use the mass of a proton (approximately 1.00728 amu) and the mass of a neutron (approximately 1.00866 amu) to find the total mass of 10 protons and 11 neutrons.

Step 3: Find the mass defect by subtracting the actual mass of the ²¹Ne nucleus (20.98846 amu) from the total mass of the separated protons and neutrons calculated in Step 2.

Step 4: Convert the mass defect into energy using Einstein's equation, E = mc², where m is the mass defect in kilograms and c is the speed of light (approximately 3.00 x 10^8 m/s). Remember to convert amu to kg (1 amu = 1.660539 x 10^-27 kg).

Step 5: Calculate the nuclear binding energy for 1 mol of ²¹Ne by multiplying the energy per nucleus by Avogadro's number (approximately 6.022 x 10^23 mol^-1).

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Nuclear Binding Energy

Nuclear binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It is a measure of the stability of a nucleus; the higher the binding energy, the more stable the nucleus. This energy can be calculated using the mass defect, which is the difference between the mass of the individual nucleons and the mass of the nucleus itself, converted into energy using Einstein's equation, E=mc².

Mass Defect

The mass defect refers to the difference in mass between a nucleus and the sum of the masses of its individual protons and neutrons. This discrepancy arises because some mass is converted into energy when nucleons bind together, resulting in a lower mass for the nucleus. Understanding the mass defect is crucial for calculating the binding energy, as it directly influences the amount of energy needed to break the nucleus apart.

Molar Binding Energy

Molar binding energy is the binding energy per mole of nuclei, providing a macroscopic measure of nuclear stability. It is calculated by multiplying the binding energy of a single nucleus by Avogadro's number (approximately 6.022 x 10²³). This concept is essential for understanding the energy involved in nuclear reactions on a larger scale, such as in nuclear power or astrophysical processes.