Nuclear Reactions and Their Applications

A sample of AgCl emits  175Ci/g . A saturated solution prepared from the solid emits $1.25\times {10}^{-2} Bq/mL$  due to radioactive AG  ions. What is the molar solubility of AGCL  ?

Question: Which nuclide(s) would you predict to be stable? Why?

(a) ${}_{\mathbf{\text{8}}}{}^{\mathbf{\text{20}}}\mathbf{\text{O}}$

(b) ${}_{\mathbf{\text{27}}}{}^{\mathbf{\text{59}}}\mathbf{\text{Co}}$

(c) ${}_{\mathbf{\text{3}}}{}^{\mathbf{\text{9}}}\mathbf{\text{Li}}$

Question: Which nuclide(s) would you predict to be stable? Why?

(a) ${}_{\mathbf{\text{60}}}{}^{\mathbf{\text{146}}}\mathbf{\text{Nd}}$

(b) ${}_{\mathbf{\text{48}}}{}^{\mathbf{\text{114}}}\mathbf{\text{Cd}}$

(c) ${}_{\mathbf{\text{42}}}{}^{\mathbf{\text{88}}}\mathbf{\text{Mo}}$

Question: Write balanced nuclear equations for the following:

(a) Alpha decay of 

(b) Electron capture by neptunium-

(c) Positron emission by 

Question: Which nuclide(s) would you predict to be stable? Why?

(a) ${}^{\mathbf{48}}\mathbf{ }\mathbf{\text{K}}$

(b)  ${}^{\mathbf{79}}\mathbf{\text{Br}}$

(c) $\mathbf{argon}-\mathbf{32}$

Question: What is the most likely mode of decay for each?

$$\begin{gathered} {\mathbf{\text{(a) }}}_{\mathbf{92}}^{\mathbf{238}}\mathbf{\text{U}} \\ {\mathbf{\text{(b) }}}_{\mathbf{24}}^{\mathbf{48}}\mathbf{\text{Cr}} \\ {\mathbf{\text{(c) }}}_{\mathbf{25}}^{\mathbf{50}}\mathbf{\text{Mn}} \end{gathered}$$

Question: What is the most likely mode of decay for each?

(a) ${}_{\mathbf{47}}{}^{\mathbf{111}}\mathbf{\text{Ag}}$

(b)  ${}_{\mathbf{17}}{}^{\mathbf{41}}\mathbf{\text{Cl}}$

(c)  ${}_{\mathbf{44}}{}^{\mathbf{110}}\mathbf{\text{Ru}}$

Question: What is the most likely mode of decay for each?

(a)  ${}^{\mathbf{15}}\mathbf{\text{C}}$

(b)   ${}^{\mathbf{120}}\mathbf{\text{Xe}}$

(c) ${}^{\mathbf{224}}\mathbf{\text{Th}}$

Question: What is the most likely mode of decay for each?

(a) ${}^{\mathbf{106}}\mathbf{\text{In}}$

(b) ${}^{\mathbf{141}}\mathbf{\text{Eu}}$

(c) ${}^{\mathbf{241}}\mathbf{\text{Am}}$

Question: Why is ${}_{\mathbf{\text{24}}}{}^{\mathbf{\text{52}}}\mathbf{\text{Cr}}$ the most stable isotope of chromium?

Question:  Why is ${}_{\mathbf{\text{20}}}{}^{\mathbf{\text{40}}}\mathbf{\text{Ca}}$ the most stable isotope of calcium?

Question: ${}^{\mathbf{237}}\mathit{N}\mathit{p}$ is the parent nuclide of a decay series that starts with  $\mathbf{\alpha }$-emission, followed by   ${\mathbf{\beta }}^{\mathbf{-}}$ emission, and then two more emissions. Write a balanced nuclear equation for each step?

Question: Why is helium found in deposits of uranium and thorium ores? What kind of radioactive emission produces it?

Question: In a natural decay series, how many $\mathit{\alpha }$ and ${\mathit{\beta }}^{\mathbf{-}}$ emissions per atom of uranium-235 result in an atom of lead-207?

Question: What electronic process is the basis for detecting radioactivity in (a) a scintillation counter; (b) a Geiger-Müller counter?

Question: What is the reaction order of radioactive decay? Explain.

Question: After 1 minute, three radioactive nuclei remain from an original sample of six. Is it valid to conclude that ${\mathit{t}}_{\mathbf{1}\mathbf{/}\mathbf{2}}$ equals 1 minute? Is this conclusion valid if the original sample contained $\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{12}}$ nuclei and $\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{12}}$ remain after 1 minute? Explain.

Question: Radioisotopic dating depends on the constant rate of decay and formation of various nuclides in a sample. How is the proportion of ${}^{\mathbf{14}}\mathbf{\text{C}}$ kept relatively constant in living organisms?

Question: What is the specific activity (in $\mathbf{\text{Ci}}\mathbf{/}\mathbf{\text{g}}$) if 1.65 mg of an isotope emits $\mathbf{1}\mathbf{.}\mathbf{56}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathit{\alpha }$ particles per second?

Why might it be difficult to use only a nuclide's $\mathit{N}\mathbf{/}\mathit{Z}$ ratio to predict whether it will decay by ${\mathit{\beta }}^{\mathbf{+}}$emission or by ${\mathbf{\text{e}}}^{\mathbf{-}}$capture? What another factor is important?

Write balanced nuclear equations for the following:

(a) Alpha decay of ${}_{\mathbf{92}}^{\mathbf{234}}\mathbf{\text{U}}$

(b) Electron capture by neptunium-232

(c) Positron emission by${}_{\mathbf{7}}^{\mathbf{12}}\mathbf{ }\mathbf{\text{N}}$

Write balanced nuclear equations for the following:

(a) ${\mathbf{\text{β}}}^{\mathbf{\text{-}}}$decay of sodium-$\mathbf{26}$

(b) ${\mathbf{\text{β}}}^{\mathbf{\text{-}}}$decay of francium- 223

(c) Alpha decay of ${}_{\mathbf{83}}^{\mathbf{212}}\mathbf{\text{Bi}}$

Write balanced nuclear equations for the following:

(a) ${\mathbf{\text{β}}}^{\mathbf{\text{-}}}$emission by magnesium-27

(b) ${\text{β}}^{\text{+}}$emission by ${}_{\mathbf{12}}^{\mathbf{23}}\mathbf{\text{Mg}}$

(c) Electron capture by${}_{\mathbf{46}}^{\mathbf{103}}\mathbf{\text{Pd}}$

Write balanced nuclear equations for the following:

(a) ${\mathit{\beta }}^{\mathbf{-}}$decay of silicon-$\mathbf{32}$

(b) Alpha decay of polonium 218

(c) Electron capture by${}_{\mathbf{49}}^{\mathbf{110}}\mathbf{\text{In}}$

Write balanced nuclear equations for the following:

1. Formation of  ${}_{\mathbf{22}}^{\mathbf{48}}\mathbf{\text{Ti}}$through positron emission 
2.  Formation of silver- 107 through electron capture
3. Formation of polonium- 206 through  decay

Write balanced nuclear equations for the following:

(a) Formation of ${}_{\mathbf{95}}^{\mathbf{241}}\mathbf{\text{Am}}$ through${\mathbf{\text{β}}}^{\mathbf{\text{-}}}$ decay

(b) Formation of  ${}_{\mathbf{89}}^{\mathbf{228}}\mathbf{\text{Ac}}$through ${\mathbf{\text{β}}}^{\mathbf{\text{-}}}$ decay

(c) Formation of ${}_{\mathbf{83}}^{\mathbf{203}}\mathbf{\text{Bi}}$ through $\mathbf{\text{α}}$ decay

Write balanced nuclear equations for the following:

(a) Formation of ${}^{186}\text{Ir}$ through electron capture

(b) Formation of francium- 221 through  decay

(c) Formation of iodine- 129 through ${\mathbf{\text{β}}}^{\mathbf{\text{-}}}$decay.

Write balanced nuclear equations for the following:

(a) Formation of  through positron emission

(b) Formation of polonium-215 through  decay

(c) Formation of  through electron capture

Determine the missing species in these transmutations, and write a full nuclear equation from the shorthand notation:

_{${\mathbf{\text{ (a) }}}^{\mathbf{\text{10}}}\mathbf{\text{ B(α,n)}}$}

$\begin{array}{l}{\mathbf{\text{(b)}}}^{\mathbf{\text{28}}}{\mathbf{\text{Si(d,)}}}^{\mathbf{\text{29}}}{\mathbf{\text{P(whered is a duteron,}}}^{\mathbf{\text{2}}}{\mathbf{\text{H}}}^{\mathbf{\text{+}}}\mathbf{\text{)}}\\ {\mathbf{\text{(c)(α,2n)}}}^{\mathbf{\text{244}}}\mathbf{\text{Cf}}\end{array}$

A  $\text{70}$.-kg person exposed to $\text{90}$ Sr absorbs  ${\mathbf{\text{6x10}}}^{\mathbf{\text{5}}}\mathbf{\text{β}}$particles, each with an nergy of ${\mathbf{\text{8.74x10}}}^{\mathbf{\text{-14}}}$ J. 

(a) How many grays does the person receive? 

(b) If the RBE is $\mathbf{\text{1.0}}$ , how many millirems is this? 

(c) What is the equivalent dose in sieverts (Sv)?

A laboratory rat weighs  $\mathbf{\text{265}}$ g and absorbs data-custom-editor="chemistry" ${\mathbf{\text{1.77×10}}}^{\mathbf{\text{10}}}{\mathbf{\text{β}}}^{\mathbf{\text{-}}}$ particles, each with an energy of data-custom-editor="chemistry" ${\mathbf{\text{2.20×10}}}^{\mathbf{\text{-13}}}$ J. 

(a) How many rads does the animal receive? 

(b) What is this dose in Gy? 

(c) If the RBE is  $\mathbf{\text{0.75}}$, what is the equivalent dose in Sv?

A  $\mathbf{\text{3.6}}$-kg laboratory animal receives a single dose of  data-custom-editor="chemistry" ${\mathbf{\text{8.92×10}}}^{\mathbf{\text{-4}}}$Gy. 

(a) How many rads did the animal receive?

 (b) How many joules did the animal absorb?

A  $\mathbf{\text{135}}$-lb person absorbs  ${\mathbf{\text{3.3×10}}}^{\mathbf{\text{-7}}}\mathbf{\text{ J}}$of energy from radioactive emissions. 

(a) How many rads does she receive? 

(b) How many grays (Gy) does she receive? 

Why is .OH more dangerous than ${\mathbf{OH}}^{-}$  in an organism?

Why is ionizing radiation more harmful to children than adults?

Elements $\mathbf{\text{104, 105, and 106}}$ have been named rutherfordium (Rf), dubnium (Db), and seaborgium (Sg), respectively. These elements are synthesized from californium-  $\mathbf{\text{249}}$by bombarding with carbon- $\mathbf{\text{12}}$, nitrogen- , and oxygen- $\mathbf{\text{18}}$ nuclei, respectively. Four neutrons are formed in each reaction as well. 

(a) Write balanced nuclear equations for the formation of these elements. 

(b) Write the equations in shorthand notation.

What is a cation-electron pair, and how does it form?

The effects on matter of  rays and  particles differ. Explain

Why does bombardment with protons usually require higher energies than bombardment with neutrons?

Why must the electrical polarity of the tubes in a linear accelerator be reversed at very short time intervals?

Early workers mistakenly thought neutron beams were   radiation. Why? What evidence led to the correct conclusion?

Irene and Frederic Joliot-Curie converted ${}_{\text{13}}^{\text{27}}$ Al to  ${}_{\mathbf{\text{15}}}^{\mathbf{\text{30}}}$P in . Why was this transmutation significant?

A rock that contains${\mathbf{\text{3.1×10}}}^{\mathbf{\text{-15}}}$  mol of ${}^{\mathbf{\text{232}}}\mathbf{\text{Th}}$  ( ${\mathbf{\text{t}}}_{\mathbf{\text{1/2}}}{\mathbf{\text{=1.4×10}}}^{\mathbf{\text{10}}}\mathbf{\text{yr}}$) has  ${\mathit{\text{9.5×10}}}^{\mathit{\text{4}}}$fission tracks, each track representing the fission of one atom of  ${}^{\mathbf{\text{232}}}\mathbf{\text{Th}}$. How old is the rock?

Plutonium-$\mathbf{\text{239}}$ $\mathbf{\left(}{\mathbf{\text{t}}}_{\mathbf{\text{1/2}}}{\mathbf{\text{=2.41×10}}}^{\mathbf{\text{4}}}\mathbf{\text{yr}}\mathbf{\right)}$ represents a serious nuclear waste hazard. If seven half-lives are required to reach a tolerable level of radioactivity, how long must  ${}^{\mathbf{\text{239}}}\mathbf{\text{Pu}}$ be stored?

Due to decay of ${}^{\mathbf{40}}\mathit{K}$ , cow’s milk has a specific activity of about ${\mathbf{\text{6x10}}}^{\mathbf{\text{-11}}}$ mCi per milliliter. How many disintegrations of ${}^{\mathbf{40}}\mathit{K}$  nuclei are there per minute in an $\mathbf{\text{8.0}}$ -oz glass of milk?

A fabric remnant from a burial site has a ${}^{\mathbf{\text{14}}}{\mathbf{\text{C/}}}^{\mathbf{\text{12}}}\mathbf{\text{C}}$  ratio of  $\mathbf{\text{0.735}}$of the original value. How old is the fabric?

A rock contains   _{$\mathbf{\mu }$}mol of ${}^{\mathbf{\text{238}}}\mathbf{\text{U}}\mathbf{\left(}{\mathbf{\text{t}}}_{\mathbf{\text{1/2}}}{\mathbf{\text{=4.5×10}}}^{\mathbf{\text{9}}}\mathbf{\text{yr}}\mathbf{\right)}$   and  110 mol of ${}^{\mathbf{\text{206}}}\mathbf{\text{ Pb}}$ Assuming that all the ${}^{\mathbf{\text{206}}}\mathbf{\text{ Pb}}$ comes from decay of the  , estimate the rock’s age.

The half-life of radium- $\text{226}$ is  $\mathbf{\text{1.60}}\mathbf{\times }{\mathbf{\text{10}}}^{\mathbf{\text{3}}}$yr. How many hours will it take for a  $\mathbf{\text{2.50}}$g sample to decay to the point where $\mathbf{\text{0.185}}$ g of the isotope remains?

The isotope  ${{}^{212}}_{83}\mathbf{Bi}$ has a half-life of $\mathbf{\text{1.01}}$ yr. What mass (in mg) of a $\mathbf{\text{2.00}}$ -mg sample will remain after ${\mathbf{\text{3.75×10}}}^{\mathbf{\text{3}}}\mathbf{\text{ h}}$ ?

A steel part is treated to form some iron-59 . Oil used to lubricate the part emits298  particles (with the energy characteristic of  ${}^{\mathbf{\text{59}}}\mathbf{\text{Fe}}$) per minute per milliliter of oil. What other information would you need to calculate the rate of removal of the steel from the part during use?