Question Detail
Question
Find the mass defect of ⁶³Cu if the actual mass of copper is 62.91367u.
Rest mass of electron (m_e) = 9.11 × 10⁻³¹ kg (0.00054858 amu)
Rest mass of proton (m_p) = 1.66 × 10⁻²⁷ kg (1.007276 amu)
Rest mass of neutron (m_n) = 1.67 × 10⁻²⁷ kg (1.008665 amu)
Rest mass of Hydrogen atom (M_H) = 1.007825 u
Rest mass of electron (m_e) = 9.11 × 10⁻³¹ kg (0.00054858 amu)
Rest mass of proton (m_p) = 1.66 × 10⁻²⁷ kg (1.007276 amu)
Rest mass of neutron (m_n) = 1.67 × 10⁻²⁷ kg (1.008665 amu)
Rest mass of Hydrogen atom (M_H) = 1.007825 u
Correct Answer
Option C is the correct answer.
Detailed Explanation
A ⁶³Cu atom has 29 protons (Z=29) and 63 - 29 = 34 neutrons (N=34).To calculate the expected mass of the constituent particles:Mass of 29 protons = 29 × 1.007276 amu = 29.211004 amuMass of 34 neutrons = 34 × 1.008665 amu = 34.294610 amuSum of masses of protons and neutrons = 29.211004 + 34.294610 = 63.505614 amu(Note: In some mass defect calculations, the mass of electrons is also added to the constituent mass, or the mass of hydrogen atoms (proton + electron) is used. However, the option suggests that the calculation based solely on protons and neutrons matches the provided choices.)Actual mass of ⁶³Cu = 62.91367 uMass defect = (Sum of masses of constituent particles) - (Actual mass of atom)Mass defect = 63.505614 amu - 62.91367 amu = 0.591944 amu.This value is very close to option C: 0.59223u (the slight difference could be due to rounding in the provided constants or options).
Hint
The mass defect is the difference between the total mass of the individual constituent nucleons (protons and neutrons) and the actual measured atomic mass.