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Chapter 2: Problem 42

The mass of a carbon-12 atom is taken to be exactly 12 u. Are there likely to be any other atoms with an exact integral (whole number) mass, expressed in u? Explain.

Short Answer

Expert verified
Although the atomic mass of a carbon-12 atom is defined as exactly 12u, there are no other atoms with an exact whole-number atomic mass when expressed in u. This is because atomic mass is a weighted average of the masses of an element's different isotopes, and the masses of protons and neutrons are not exactly 1u each. Therefore, atomic mass expressed in u would not be exactly integral, apart from carbon-12.

Step by step solution

01

Understanding Atomic Mass Units

To understand the problem, first it is necessary to know what an atomic mass unit is. It is a unit of mass used to express atomic and molecular weights, where the carbon-12 atom is taken as the standard and assigned a value of 12u. This means 1u is 1/12 of the mass of a carbon-12 atom.
02

Clarifying Exact Integral Atomic Mass

The atomic mass of any atom, expressed in u, is not an exact integer number (except for carbon-12), due to the presence of various isotopes with different numbers of neutrons, and the fact that the mass of a neutron and a proton are not exactly 1u. Therefore, the atomic mass of an element is a weighted average of the masses of all the naturally occurring isotopes. Thus, atomic masses are usually not whole numbers.
03

Reason for Non-Integral Atomic Mass

To understand why atomic masses are not usually exact integers, we must remember that an atom's total mass is contributed by protons, neutrons, and electrons. While the masses of protons and neutrons are each roughly 1u, they are not exactly 1u. Moreover, electrons also contribute, albeit a far smaller amount, to the total atomic mass. What's more, every element has various isotopes, which means that the atomic mass is indeed a weighted average of the isotopes. These factors result in atomic masses that are not exact integers.

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Most popular questions from this chapter

William Prout (1815) proposed that all other atoms are built up of hydrogen atoms, suggesting that all elements should have integral atomic masses based on an atomic mass of one for hydrogen. This hypothesis appeared discredited by the discovery of atomic masses, such as 24.3 u for magnesium and 35.5 u for chlorine. In terms of modern knowledge, explain why Prout's hypothesis is actually quite reasonable.

In one experiment, the burning of \(0.312 \mathrm{g}\) sulfur produced 0.623 g sulfur dioxide as the sole product of the reaction. In a second experiment, \(0.842 \mathrm{g}\) sulfur dioxide was obtained. What mass of sulfur must have been burned in the second experiment?

What is the total number of atoms in (a) 15.8 mol \(\mathrm{Fe}\); (b) \(0.000467 \mathrm{mol} \mathrm{Ag} ;\) (c) \(8.5 \times 10^{-11} \mathrm{mol} \mathrm{Na} ?\)

Use fundamental definitions and statements from Chapters 1 and 2 to establish the fact that \(6.022 \times 10^{23} \mathrm{u}=1.000 \mathrm{g}\)

To four significant figures, all of the following masses are possible for an individual titanium atom except one. The exception is (a) 45.95 u; (b) 46.95 u; (c) 47.87 u; (d) 47.95 u; (e) 48.95 u; (f) 49.94 u.
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