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Chapter 1: Problem 23

For lighter, stable isotopes, the ratio of the mass number to the atomic number is close to a certain value. What is the value? What happens to the value of the mass number to atomic number ratio as stable isotopes become heavier?

Short Answer

Expert verified
For lighter, stable isotopes, the ratio of the mass number (A) to the atomic number (Z) is approximately 2, meaning \(\frac{A}{Z} \approx 2\). As stable isotopes become heavier, the ratio \(\frac{A}{Z}\) increases due to the need for more neutrons to maintain stability in the nucleus against the stronger electrostatic repulsion caused by a larger number of protons.

Step by step solution

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1. Determining the ratio for lighter, stable isotopes

For lighter, stable isotopes, the ratio of the mass number (A) to the atomic number (Z) is approximately 2. This means that the mass number (number of protons and neutrons) is twice the atomic number (number of protons): \[ \frac{A}{Z} \approx 2 \]
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2. Understanding the trend with heavier isotopes

As stable isotopes become heavier, the ratio \(\frac{A}{Z}\) increases. This is because adding more neutrons is necessary to increase the stability of the nucleus for elements with a higher atomic number (more protons). The larger number of protons leads to a stronger electrostatic repulsion within the nucleus, so adding more neutrons with their strong nuclear force helps offset this repulsion and maintain stability.
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3. Conclusion

The ratio of the mass number to the atomic number for lighter, stable isotopes is approximately 2. As the isotopes become heavier, the value of this ratio increases due to the need for an increased number of neutrons for stability.

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Most popular questions from this chapter

Which of the following statements is/are true? For the false statements, correct them. a. All particles in the nucleus of an atom are charged. b. The atom is best described as a uniform sphere of matter in which electrons are embedded. c. The mass of the nucleus is only a very small fraction of the mass of the entire atom. d. The volume of the nucleus is only a very small fraction of the total volume of the atom. e. The number of neutrons in a neutral atom must equal the number of electrons.

Write the atomic symbol \(\left(\frac{1}{2} X\right)\) for each of the isotopes described below. a. number of protons \(=27,\) number of neutrons \(=31\) b. the isotope of boron with mass number 10 c. \(Z=12, A=23\) d. atomic number \(53,\) number of neutrons \(=79\) e. \(Z=20,\) number of neutrons \(=27\) f. number of protons \(=29,\) mass number 65

In a combustion reaction, \(46.0 \mathrm{g}\) of ethanol reacts with \(96.0 \mathrm{g}\) of oxygen to produce water and carbon dioxide. If \(54.0 \mathrm{g}\) of water is produced, what mass of carbon dioxide is produced?

The isotope of an unknown element, \(\mathrm{X},\) has a mass number of 79\. The most stable ion of this isotope has 36 electrons and has a \(2-\) charge. Which of the following statements is(are) true? For the false statements, correct them. a. This ion has more electrons than protons in the nucleus. b. The isotope of \(X\) contains 38 protons. c. The isotope of \(X\) contains 41 neutrons. d. The identity of \(\mathrm{X}\) is strontium, \(\mathrm{Sr}\).

When mixtures of gaseous \(\mathrm{H}_{2}\) and gaseous \(\mathrm{Cl}_{2}\) react, a product forms that has the same properties regardless of the relative amounts of \(\mathrm{H}_{2}\) and \(\mathrm{Cl}_{2}\) used. a. How is this result interpreted in terms of the law of definite proportion? b. When a volume of \(\mathrm{H}_{2}\) reacts with an equal volume of \(\mathrm{Cl}_{2}\) at the same temperature and pressure, what volume of product having the formula HCl is formed?
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