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Chapter 2: Problem 26

(a) Which two of the following are isotopes of the same element: \(\frac{31}{16} \mathrm{X}, \frac{31}{15} \mathrm{X}, \frac{32}{16} \mathrm{X}\) ? (b) What is the identity of the element whose isotopes you have selected?

Short Answer

Expert verified
(a) The two isotopes of the same element are \(\frac{31}{16} \mathrm{X}\) and \(\frac{32}{16} \mathrm{X}\), since they both have the same atomic number, Z = 16. (b) The element with atomic number 16 is Sulfur (S), so the isotopes are \(\frac{31}{16}\mathrm{S}\) and \(\frac{32}{16}\mathrm{S}\).

Step by step solution

01

Understanding the notation

The notation for an isotope is given as \(\frac{A}{Z}\mathrm{X}\), where A represents the mass number (number of protons and neutrons), Z represents the atomic number (number of protons), and X is the symbol of the element. To identify isotopes of the same element, we need to compare the atomic numbers (Z) of each given option.
02

Compare atomic numbers

We have the following isotopes given in the exercise: 1. \(\frac{31}{16} \mathrm{X}\) 2. \(\frac{31}{15} \mathrm{X}\) 3. \(\frac{32}{16} \mathrm{X}\) Comparing the atomic numbers (Z), we can see that option 1 and option 3 have the same atomic number (Z = 16). So, these two are isotopes of the same element.
03

Identify the element

Now that we know that \(\frac{31}{16} \mathrm{X}\) and \(\frac{32}{16} \mathrm{X}\) are isotopes of the same element, we need to determine the identity of this element. The atomic number (Z) determines the identity of the element. The atomic number (Z) for both these isotopes is 16. We know that an element with atomic number 16 is Sulfur (symbol S). So, the isotopes are: 1. \(\frac{31}{16}\mathrm{S}\) 2. \(\frac{32}{16}\mathrm{S}\)

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Most popular questions from this chapter

One way in which Earth's evolution as a planet can be understood is by measuring the amounts of certain isotopes in rocks. One quantity recently measured is the ratio of 1129 \(\mathrm{Xe}\) to \(^{130} \mathrm{Xe}\) in some minerals. In what way do these two isotopes differ from one another? In what respects are they the same?

The element oxygen has three naturally occurring isotopes, with \(8,9,\) and 10 neutrons in the nucleus, respectively. (a) Write the full chemical symbols for these three isotopes. (b) Describe the similarities and differences between the three kinds of atoms of oxygen.

A cube of gold that is 1.00 \(\mathrm{cm}\) on a side has a mass of 19.3 \(\mathrm{g}\) A single gold atom has a mass of 197.0 amu. (a) How many gold atoms are in the cube? (b) From the information given,estimate the diameter in \(A\) of a single gold atom. (c) What assumptions did you make in arriving at your answer for part (b)?

A 1.0 -g sample of carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) is fully decomposed into its elements, yielding 0.273 g of carbon and 0.727 \(\mathrm{g}\) of oxygen. (a) What is the ratio of the mass of \(\mathrm{O}\) to \(\mathrm{C} ?\) (b) If a sample of a different compound decomposes into 0.429 \(\mathrm{g}\) of carbon and 0.571 \(\mathrm{g}\) of oxygen, what is its ratio of the mass of \(\mathrm{O}\) to \(\mathrm{C} ?(\mathbf{c})\) According to Dalton's atomic theory, what is the empirical formula of the second compound?

The explosion of an atomic bomb releases many radioactive isotopes, including strontium- \(90 .\) Considering the location of strontium in the periodic table, suggest a reason for the fact that this isotope is particularly dangerous for human health.
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