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Chapter 22: Problem 57

What are the products of radioactive decay of \(^{137} \mathrm{Cs} ?\) Write a balanced equation for the nuclear decay reaction.

Short Answer

Expert verified
Answer: The radioactive decay of Cesium-137 (Cs-137) results in the creation of Barium-137 (Ba-137), a beta particle (electron), and an electron antineutrino. The balanced nuclear decay equation for this process would be: $$^{137}\mathrm{Cs} \rightarrow ^{137}\mathrm{Ba} + e^- + \bar{\nu}_e$$

Step by step solution

01

Identify the type of radioactive decay

In this case, \(^{137}\mathrm{Cs}\) undergoes beta decay, which means that a neutron within the nucleus will be converted into a proton, releasing an electron (also called a beta particle) and an electron antineutrino.
02

Determine the products of the decay

As a result of beta decay, we will have one more proton and one fewer neutron in the nucleus. Since atomic number (number of protons) determines the element, we can predict that in the case of \(^{137}\mathrm{Cs}\), the resulting element will be Barium (\(\mathrm{Ba}\)) with an atomic number one higher than Cesium. The new nucleus will consist of 56 protons and 81 neutrons (137-56). The decay also produces a beta particle (electron) and an electron antineutrino, which are represented by \(e^-\) and \(\bar{\nu}_e\), respectively.
03

Write the balanced nuclear decay equation

To write the balanced nuclear decay equation, we should make sure that the sum of the atomic masses and atomic numbers on both sides of the equation are equal. Atomic masses: \(137 (\mathrm{Cs}) = 137 (\mathrm{Ba})\) Atomic numbers: \(55 (\mathrm{Cs}) = 56 (\mathrm{Ba}) -1 (e^-)\) Considering these balances, we can now write the balanced nuclear decay equation for the radioactive decay of \(^{137}\mathrm{Cs}\): $$^{137}\mathrm{Cs} \rightarrow ^{137}\mathrm{Ba} + e^- + \bar{\nu}_e$$

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Most popular questions from this chapter

In the human body, the concentrations of ultratrace essential elements are even lower than those of trace essential elements and therefore are sometimes expressed in parts per billion. Express the concentrations of each of the following elements in parts per billion: a. Bromine, \(6 \mathrm{mg} / \mathrm{L}\) b. Boron, \(0.014 \mathrm{g} / 100 \mathrm{kg}\) c. Selenium, \(5.0 \mathrm{mg} / 70 \mathrm{kg}\)

The antacid known as Maalox contains a mixture of magnesium and aluminum hydroxides. Which substance will neutralize more acid on a per mole basis? Does the same substance also neutralize more acid on a per gram basis?

Place the following ions in order of increasing ionic radius: \(\mathrm{Mg}^{2+}, \mathrm{Li}^{+}, \mathrm{Al}^{3+},\) and \(\mathrm{Cl}^{-}.\)

Ion Transport in Cells Describe three ways in which ions of major essential elements (such as \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) ) enter and exit cells.

Potassium- 40 decays by three pathways: \(\beta\) decay, positron emission, and electron capture. Write balanced equations for each of these processes.
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