The atomic mass of ^127 53I is 126.9004 amu. Calculate the nuclear binding energy of this nucleus and the corresponding nuclear binding energy per nucleon. Strategy To calculate the nuclear binding energy, we first determine the difference between the mass of the nucleus and the mass of all the

Question

The atomic mass of [latex]^{127}_{53} I [/latex] is 126.9004 amu. Calculate the nuclear binding energy of this nucleus and the corresponding nuclear binding energy per nucleon.

Strategy To calculate the nuclear binding energy, we first determine the difference between the mass of the nucleus and the mass of all the protons and neutrons, which gives us the mass defect. Next, we apply Equation (19.2)[latex] [ΔE = (Δm)c^{2}][/latex].

Accepted Answer

There are 53 protons and 74 neutrons in the iodine nucleus. The neutron- toproton ratio is 1.4, which places iodine-127 in the belt of stability. The mass of [latex]^{1}_{1} H [/latex] atom is

53 × 1.007825 amu = 53.41473 amu

and the mass of 74 neutrons is

74 × 1.008665 amu = 74.64121 amu

Therefore, the predicted mass for [latex]^{127}_{53} I [/latex] is 53.41473 + 74.64121 = 128.05594 amu, and the mass defect is

Δm = 126.9004 amu - 128.05594 amu

= -1.1555 amu

The energy released is

[latex] ΔE = (Δm)c^{2}[/latex]

[latex]=(-1.1555 amu)(3.00 imes 10^{8} m/s)²[/latex]

[latex]=-1.04 imes 10^{17} amu . m²/s²[/latex]

Let’s convert to a more familiar energy unit of joules. Recall that 1 J = 1 kg · m²/s². Therefore, we need to convert amu to kg:

[latex]ΔE =-1.04 imes 10^{17}\frac{\cancel{amu} . m²}{s²} imes \frac{1.00 \cancel{g}}{6.022 imes 10^{23} \cancel{ amu} } imes \frac{1 kg}{1000 \cancel{g}} [/latex]

[latex]=-1.73 imes 10^{-10} \frac{kg ⋅ m²}{s²}=-1.73 imes 10^{-10} J[/latex]

Thus, the nuclear binding energy is [latex]1.73 imes 10^{-10} J[/latex] . The nuclear binding energy per nucleon is obtained as follows:

[latex]\frac{1.73 imes 10^{-10} J}{127 nucleons}=1.36 imes 10^{-12} J/nucleon[/latex]

Question 19.2: The atomic mass of ^127 53I is 126.9004 amu. Calculate the n...

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