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Chapter 2: Problem 74

Determine the only possible isotope (E) for which the following conditions are met: \(\bullet\)The mass number of \(\mathrm{E}\) is 2.50 times its atomic number. \(\bullet\)The atomic number of \(\mathrm{E}\) is equal to the mass number of another isotope (Y). In turn, isotope Y has a neutron number that is 1.33 times the atomic number of \(Y\) and equal to the neutron number of selenium- 82 .

Short Answer

Expert verified
The isotope E that fits the given conditions is silicon-36 (Si-36).

Step by step solution

01

Define the known and unknown variables

Let's denote the atomic number of isotope E as Z1 and its mass number as A1. The atomic number 'Z' and the mass number 'A' for Y are Z2 and A2 respectively. From the given conditions, the following relationships are obtained: A1 = 2.5 * Z1, Z2 = A1, and Number of neutrons in Y = 1.33 * Z2 = 48.
02

Solve the equations

By plugging Z2 = A1 into the third equation gives 1.33 * A1 = 48. Solving for A1 gives A1 = 48 / 1.33, which results in A1 = 36 (rounded to the nearest whole number).
03

Determine the atomic number of E

Knowing the value of A1, we can use the equation A1 = 2.5 * Z1 to calculate Z1. Substituting A1 = 36 into the equation gives Z1 = A1 / 2.5, which results in Z1 = 36 / 2.5 = 14.4, roughly rounded to the nearest whole number gives Z1 = 14.
04

Identify isotope E

From the periodic table, the element with the atomic number 14 is silicon (Si). So, the isotope E is silicon-36 (Si-36).

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Most popular questions from this chapter

Assuming that the seventh period of the periodic table has 32 members, what should be the atomic number of (a) the noble gas following radon (Rn); (b) the alkali metal following francium (Fr)?

There are three common iron-oxygen compounds. The one with the greatest proportion of iron has one Fe atom for every \(\mathrm{O}\) atom and the formula \(\mathrm{FeO}\). A second compound has 2.327 g Fe per \(1.000 \mathrm{g} \mathrm{O},\) and the third has \(2.618 \mathrm{g}\) Fe per \(1.000 \mathrm{g}\) O. What are the formulas of these other two iron-oxygen compounds?

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