교과서 질문
How much energy (in kJ/mol) is released in the fusion reaction of 1H and 2H atoms?
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21. Nuclear Chemistry
Nuclear Binding Energy
객관식
Calculate the total binding energy (in MeV) for the isotope 127I, given that the atomic mass is 126.90447 u and the atomic number is 53.
A
1048 MeV
B
980 MeV
C
1150 MeV
D
1120 MeV
검증된 단계별 안내1
Understand the concept of binding energy: Binding energy is the energy required to disassemble a nucleus into its individual protons and neutrons. It is a measure of the stability of a nucleus.
Calculate the mass defect: The mass defect is the difference between the sum of the masses of the protons and neutrons and the actual mass of the nucleus. Use the formula: \( \text{Mass defect} = (Z \times m_p + N \times m_n) - m_{\text{nucleus}} \), where \( Z \) is the atomic number, \( m_p \) is the mass of a proton, \( N \) is the number of neutrons, \( m_n \) is the mass of a neutron, and \( m_{\text{nucleus}} \) is the atomic mass of the isotope.
Determine the number of neutrons: For the isotope \( ^{127}\text{I} \), the number of neutrons \( N \) can be calculated using \( N = A - Z \), where \( A \) is the mass number (127 for iodine) and \( Z \) is the atomic number (53 for iodine).
Convert the mass defect to energy: Use Einstein's equation \( E = \Delta m \times c^2 \) to convert the mass defect from atomic mass units (u) to energy in MeV. The conversion factor is \( 1 \text{ u} = 931.5 \text{ MeV/c}^2 \).
Calculate the total binding energy: The total binding energy is the energy equivalent of the mass defect calculated in the previous step. This will give you the binding energy in MeV for the isotope \( ^{127}\text{I} \).
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