Calculate the mass defect and the nuclear binding energy for an α particle (helium nucleus).

Question

Calculate the mass defect and the nuclear binding energy for an [latex]\alpha[/latex] particle (helium nucleus).

Accepted Answer

Knowns: proton mass = 1.0073 g/mol

neutron mass = 1.0087 g/mol

[latex]\alpha[/latex] mass = 4.0015 g/mol

1.0 g = 9.0 [latex] imes 10^{13} [/latex] J

PLAN First calculate the sum of the individual parts of an particle (2 protons +2 neutrons).

2 protons: 2 [latex] imes[/latex] 1.0073 g/mol = 2.0146 g/mol

2 neutrons: 2 [latex] imes[/latex] 1.0087 g/mol = 2.0174 g/mol

[latex]\overline{4.0320 g/mol}[/latex]

The mass defect is the difference between the mass of the -particle and its component parts:

4.0320 g/mol

4.0015 g/mol

[latex]\overline{0.0305 g/mol}[/latex] (mass defect)

CALCULATE To find the nuclear binding energy, convert the mass defect to its energy equivalent:

(0.0305 g/mol)(9.0 [latex] imes 10^{13}[/latex] J/g)

= 2.7 [latex] imes 10^{12} J/mol (6.5 imes 10^{11}[/latex] cal)

Question 18.5: Calculate the mass defect and the nuclear binding energy for...