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Chapter 19: Problem 15

Write an equation describing the radioactive decay of each of the following nuclides. (The particle produced is shown in parentheses, except for electron capture, where an electron is a reactant.) a.\(_{1}^{3} \mathrm{H}(\beta)\) b. \(_{3}^{8} \operatorname{Li}(\beta \text { followed by } \alpha)\) c. \(\quad_{4}^{7}\) Be (electron capture) d. \(_{5}^{8} \mathrm{B}(\text { positron })\)

Short Answer

Expert verified
The short version of the answer for each nuclide radioactive decay is: a. \[_{1}^{3} \mathrm{H} \to _{2}^{3} \mathrm{He} + \beta^{-} + \bar{\nu}_e\] b. \[_{3}^{8} \operatorname{Li} \to _{4}^{8} \mathrm{Be} + \beta^{-} + \bar{\nu}_e\] _ \[_{4}^{8} \mathrm{Be} \to _{2}^{4} \mathrm{He} + _{2}^{4} \mathrm{He}\] c. \[_{4}^{7} \mathrm{Be} + e^{-} \to _{3}^{7} \mathrm{Li} + \nu_e\] d. \[_{5}^{8} \mathrm{B} \to _{4}^{8} \mathrm{Be} + \beta^{+} + \nu_e\]

Step by step solution

01

Identify the initial nuclide and decay process

For this problem, we have Hydrogen-3 undergoing beta (β) decay. In a beta decay, the initial nuclide emits an electron (β-) and an antineutrino, converting a neutron to a proton.
02

Write the equation for the decay process

We will write the equation as follows: \[_{1}^{3} \mathrm{H} \to _{2}^{3} \mathrm{He} + \beta^{-} + \bar{\nu}_e\] #b. Beta decay followed by alpha decay of Lithium-8#
03

Recognize the initial nuclide and decay processes

For this decay, we have Lithium-8 undergoing beta (β) decay followed by alpha (α) decay. We'll handle these two decay processes separately.
04

Write the equation for the beta decay process

The initial nuclide emits an electron (β-) and an antineutrino, converting a neutron to a proton: \[_{3}^{8} \operatorname{Li} \to _{4}^{8} \mathrm{Be} + \beta^{-} + \bar{\nu}_e\]
05

Write the equation for the alpha decay process

After the beta decay, the produced Beryllium-8 undergoes an alpha decay, during which an alpha particle (Helium-4 nucleus) is emitted. \[_{4}^{8} \mathrm{Be} \to _{2}^{4} \mathrm{He} + _{2}^{4} \mathrm{He}\] #c. Electron capture of Beryllium-7#
06

Identify the initial nuclide and decay process

The initial nuclide is Beryllium-7, which undergoes electron capture. In electron capture, an inner-shell electron is captured by the nucleus and combines with a proton to form a neutron. This process also emits a neutrino.
07

Write the equation for the electron capture process

We will write the equation as follows: \[_{4}^{7} \mathrm{Be} + e^{-} \to _{3}^{7} \mathrm{Li} + \nu_e\] #d. Positron decay of Boron-8#
08

Identify the initial nuclide and decay process

The initial nuclide is Boron-8, which undergoes positron decay. In positron decay, the nucleus emits a positron (β+), i.e., an anti-electron, which converts a proton into a neutron. This process also emits a neutrino.
09

Write the equation for the positron decay process

We will write the equation as follows: \[_{5}^{8} \mathrm{B} \to _{4}^{8} \mathrm{Be} + \beta^{+} + \nu_e\]

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Most popular questions from this chapter

Do radiotracers generally have long or short half-lives? Explain.

Using the kinetic molecular theory (section \(5.6 ),\) calculate the root mean square velocity and the average kinetic energy of \(_{1}^{2} \mathrm{H}\) nuclei at a temperature of \(4 \times 10^{7} \mathrm{K}\) . (See Exercise 56 for the appropriate mass values.)

In each of the following radioactive decay processes, supply the missing particle. a. \(^{73} \mathrm{Ga} \rightarrow^{73} \mathrm{Ge}+?\) b. \(^{192} \mathrm{Pt} \rightarrow^{188} \mathrm{Os}+?\) c. \(^{205} \mathrm{Bi} \rightarrow^{205} \mathrm{Pb}+?\) d. \(^{241} \mathrm{Cm}+? \rightarrow^{241} \mathrm{Am}\)

To determine the \(K_{\mathrm{sp}}\) value of \(\mathrm{Hg}_{2} \mathrm{I}_{2},\) a chemist obtained a solid sample of \(\mathrm{Hg}_{2} \mathrm{I}_{2}\) in which some of the iodine is present as radioactive 131 \(\mathrm{I}\) . The count rate of the \(\mathrm{Hg}_{2} \mathrm{I}_{2}\) sample is \(5.0 \times 10^{11}\) counts per minute per mole of I. An excess amount of $\mathrm{Hg}_{2} \mathrm{I}_{2}(s)$ is placed into some water, and the solid is allowed to come to equilibrium with its respective ions. A \(150.0-\mathrm{mL}\) sample of the saturated solution is withdrawn and the radioactivity measured at 33 counts per minute. From this information, calculate the \(K_{\mathrm{sp}}\) value for \(\mathrm{Hg}_{2} \mathrm{I}_{2}\) $$ \mathrm{Hg}_{2} \mathrm{I}_{2}(s) \rightleftharpoons \mathrm{Hg}_{2}^{2+}(a q)+2 \mathrm{I}^{-}(a q) \qquad K_{\mathrm{sp}}=\left[\mathrm{Hg}_{2}^{2+}\right]\left[\mathrm{I}^{-}\right]^{2} $$

The first atomic explosion was detonated in the desert north of Alamogordo, New Mexico, on July \(16,1945 .\) What percentage of the strontium- 90\(\left(t_{1 / 2}=28.9 \text { years) originally produced }\right.\) by that explosion still remains as of July \(16,2017 ?\)
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