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Chapter 25: Problem 82

Of the following nuclides, the highest nuclear binding energy per nucleon is found in (a) \(_{1}^{3} \mathrm{H} ;\) (b) \(_{8}^{16} \mathrm{O} ;\) (c) \(_{26}^{56} \mathrm{Fe}\); (d) \(_{92}^{235} \mathrm{U}\).

Short Answer

Expert verified
The nuclide with the highest nuclear binding energy per nucleon is \(_{26}^{56} \mathrm{Fe}\).

Step by step solution

01

Understanding the information

The task gives us four nuclides: Tritium \(_{1}^{3} \mathrm{H}\), Oxygen \(_{8}^{16} \mathrm{O}\), Iron \(_{26}^{56} \mathrm{Fe}\), and Uranium \(_{92}^{235} \mathrm{U}\). We need to determine which one of these has the highest nuclear binding energy per nucleon.
02

Refer to the binding energy curve

The binding energy curve charts binding energy per nucleon against atomic number. First, it increases, reaching a maximum at Iron-56 (\(_{26}^{56} \mathrm{Fe}\)), then it decreases for elements with higher atomic numbers.
03

Apply knowledge of the binding energy curve to given nuclides

According to the curve, the binding energy per nucleon is highest for Iron-56 (\(_{26}^{56} \mathrm{Fe}\)), lower for elements lighter than iron like Tritium (\(_{1}^{3} \mathrm{H}\)) and Oxygen (\(_{8}^{16} \mathrm{O}\)), and even lower for heavier elements like Uranium (\(_{92}^{235} \mathrm{U}\)).

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Most popular questions from this chapter

In some cases, the most abundant isotope of an element can be established by rounding off the atomic mass to the nearest whole number, as in \(^{39} \mathrm{K},^{85} \mathrm{Rb}\), and \(^{88} \mathrm{Sr}\). But in other cases, the isotope corresponding to the rounded-off atomic mass does not even occur naturally, as in \(^{64} \mathrm{Cu}\). Explain the basis of this observation.

A lunar rock was analyzed for argon by mass spectrometry and for potassium by atomic absorption. The results of these analyses showed that the sample contained \(3.02 \times 10^{-5} \mathrm{mL} \mathrm{g}^{-1}\) of argon and \(0.083 \%\) of potassium. The half-life of potassium- 40 is \(1.248 \times\) \(10^{9} \mathrm{y} \cdot\) Calculate the age of the lunar rock.

The carbon-14 dating method is based on the assumption that the rate of production of \(^{14} \mathrm{C}\) by cosmic ray bombardment has remained constant for thousands of years and that the ratio of \(^{14} \mathrm{C}\) to \(^{12} \mathrm{C}\) has also remained constant. Can you think of any effects of human activities that could invalidate this assumption in the future?

Neutron bombardment of \(^{23}\) Na produces an isotope that is a \(\beta\) emitter. After \(\beta\) emission, the final product is (a) \(^{24} \mathrm{Na} ;\) (b) \(^{23} \mathrm{Mg} ;\) (c) \(^{23} \mathrm{Ar} ;\) (d) \(^{24} \mathrm{Ar} ;\) (e) none of these.

Assume that when Earth formed, uranium-238 and uranium-235 were equally abundant. Their current percent natural abundances are \(99.28 \%\) uranium- 238 and \(0.72 \%\) uranium- \(235 .\) Given half-lives of \(4.5 \times 10^{9}\) years for uranium-238 and \(7.1 \times 10^{8}\) years for uranium-235, determine the age of Earth corresponding to this assumption.
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