Nuclear Reactions and Their Applications

Positrons cannot penetrate matter more than a few atomic diameters, but positron emission of radiotracers can be monitored in medical diagnosis. Explain.

Why is neutron activation analysis (NAA) useful to art historians and criminologists?

What two ways are radioactive tracers used in organisms?

A small region of a cancer patient’s brain is exposed for 24.0 min to 475 Bq of radioactivity from  60Co for treatment of a tumor. If the brain mass exposed is  $\text{1.858}$g and each  particle emitted has an energy of  ${\mathbf{\text{5.05×10}}}^{\mathbf{\text{-14}}}\mathbf{\text{ J}}$, what is the dose in rads

What is the specific activity (in  $\mathbf{\text{Ci}}\mathbf{/}\mathbf{\text{g}}$ ) if  $\mathbf{2}\mathbf{.6}\mathbf{ }\mathbf{\text{g}}$of an isotope emits$\mathbf{4}\mathbf{.13}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}{\mathit{\beta }}^{\mathbf{-}}$  particles per hour?

What is the specific activity (in $\mathbf{\text{Bq}}\mathbf{/}\mathbf{\text{g}}$ ) if  $\mathbf{8}\mathbf{.58}\mathit{\mu }\mathbf{\text{g}}$ of an isotope emits  $\mathbf{7}\mathbf{.4}\mathbf{\times }{\mathbf{10}}^{\mathbf{4}}\mathit{\alpha }$particles per minute?

What is the specific activity (in  $\mathbf{\text{Bq}}\mathbf{/}\mathbf{\text{g}}$) if  of an isotope emits  $\mathbf{3}\mathbf{.77}\mathbf{\times }{\mathbf{10}}^{\mathbf{7}}{\mathit{\beta }}^{\mathbf{-}}$particles per minute?

If one-trillionth of the atoms of a radioactive isotope disintegrate each day, what is the decay constant of the process?

If $\mathbf{2}\mathbf{.8}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathit{\%}$ of the atoms of a radioactive isotope disintegrate in $\mathbf{1}\mathbf{.0}\mathbf{\text{yr}}$ , what is the decay constant of the process?

If  $\mathbf{1}\mathbf{.00}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{12}}\mathbf{ }\mathbf{\text{mol}}$of  ${}^{\mathbf{135}}\mathbf{\text{Cs}}$emits$\mathbf{1}\mathbf{.39}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}{\mathit{\beta }}^{\mathbf{-}}$  particles in $\mathbf{1}\mathbf{.00}\mathbf{\text{yr}}$ , what is the decay constant?

If $\mathbf{6}\mathbf{.40}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{ }\mathbf{\text{mol}}$  of  ${}^{\mathbf{176}}\mathbf{ }\mathbf{\text{W}}$ emits$\mathbf{1}\mathbf{.07}\mathbf{\times }{\mathbf{10}}^{\mathbf{15}}{\mathit{\beta }}^{\mathbf{+}}$ in  $\mathbf{1}\mathbf{.00}\mathbf{ }\mathbf{\text{h}}$, what is the decay constant?

Archeologists removed some charcoal from a Native American campfire, burned it in, and bubbled the ${\text{CO}}_{\text{2}}$ formed into  solution (limewater). The ${\text{CaCO}}_{\text{3}}$  that precipitated was filtered and dried. If  4.58 g of the ${\text{CaCO}}_{\text{3}}$ had a radioactivity of 3.2 d/min, how long ago was the campfire?

A $5.4-\mu$  gample of ${}^{226}RaC{l}_2$  has a radioactivity of $1.5\times {10}^5 Bq$ . Calculate $t_{1/2}$  of  ${}^{226}Ra$ .

How many rads does a 65-kg  human receive each year from the approximately  10^-8 g of ${}_6{}^{14}C$  naturally present in her body (t = 5730 yrs;   each disintegration releases 0.156MeV) ?

How many joules are released when $\mathbf{1}\mathbf{.}\mathbf{5}$ mol of  $\mathbf{239}$ Pu decays, if each nucleus releases $\mathbf{5}\mathbf{.}\mathbf{243}$ MeV?

How many MeV are released per nucleus when ${\mathbf{\text{3.2×10}}}^{\mathbf{\text{ - 3}}}\mathbf{\text{ mol}}$ of chromium-$\mathbf{49}$ releases ${\mathbf{\text{8.11×10}}}^{\mathbf{\text{5}}}\mathbf{\text{ kJ}}$? 

Oxygen-$\mathbf{16}$ is one of the most stable nuclides. The mass of a ${}^{\mathbf{\text{16}}}\mathbf{\text{O }}$atom is $\mathbf{\text{15.994915}}$amu. Calculate the binding energy 

(a) per nucleon in MeV;

(b) per atom in MeV;

 (c) per mole in kJ.

What is the binding energy per nucleon? Why is the binding energy per nucleon, rather than per nuclide, used to compare nuclide stability?

When a nucleus forms from nucleons, is energy absorbed or released? Why?

How does a change in mass arise when a nuclide forms from nucleons?

Many scientists at first reacted skeptically to Einstein’s equation, .$\mathbf{E}= {\text{mc}}_{}^{\text{2}}$ Why?

The oxidation of methanol to formaldehyde can be accomplished by reaction with chromic acid: 

 ${\mathbf{\text{6H}}}^{\mathbf{\text{+}}}{\mathbf{\text{(aq)+3CH}}}_{\mathbf{\text{3}}}{\mathbf{\text{OH(aq) +2H}}}_{\mathbf{\text{2}}}{\mathbf{\text{CrO}}}_{\mathbf{\text{4}}}\mathbf{\text{(aq)}}\mathbf{\to }{\mathbf{\text{3CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{O(aq)+2Cr}}}^{\mathbf{\text{3+}}}{\mathbf{\text{(aq)+8H}}}_{\mathbf{\text{2}}}\mathbf{\text{O(l)}}$

The reaction can be studied with the stable isotope tracer  _{${}^{\mathbf{\text{18}}}\mathbf{\text{O}}$} and mass spectrometry. When a small amount of CH318OH is present in the alcohol reactant, ${{\mathbf{\text{CH}}}_{\mathbf{\text{2}}}}^{\mathbf{\text{18}}}\mathbf{\text{O}}$  forms. When a small amount of  ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{Cr}}}^{\mathbf{\text{18}}}{\mathbf{\text{O}}}_{\mathbf{\text{4}}}$ is present,  ${{\mathbf{\text{H}}}_{\mathbf{\text{2}}}}^{\mathbf{\text{18}}}\mathbf{\text{O}}$ forms. Does chromic acid or methanol supply the O atom to the aldehyde? Explain.

Iodine-$\mathbf{\text{131}}$ is one of the most important isotopes used in the diagnosis of thyroid cancer. One atom has a mass of $\mathbf{\text{130.906114}}$amu. Calculate the binding energy 

(a) per nucleon in MeV;

 (b) per atom in MeV;

(c) per mole in kJ.

The ${}^{\mathbf{\text{80}}}\mathbf{\text{Br}}$ nuclide decays either by decay or by electron capture. 

(a) What is the product of each process? 

(b) Which process releases more energy? (Masses of atoms: ${}^{\mathbf{\text{80}}}\mathbf{\text{Br}}$=$\mathbf{\text{79.918528}}$amu; ${}_{}{}^{\mathbf{\text{80}}}\mathbf{\text{Kr}}$=$\mathbf{\text{79.916380}}$amu; ${}_{}{}^{\mathbf{\text{80}}}\mathbf{\text{Se}}\mathbf{=}\mathbf{\text{79.916520}}$amu; neglect the mass of electrons involved because these are atomic, not nuclear, masses.)

What is the minimum number of neutrons from each fission event that must be absorbed by other nuclei for a chain reaction to be sustained?

What is the purpose of enrichment in the preparation of fuel rods? How is it accomplished?

Describe the nature and purpose of these components of a nuclear reactor: 

(a) control rods.

(b) moderator.

(c) reflector.

State an advantage and a disadvantage of heavy-water reactors compared to light-water reactors.

What are the expected advantages of fusion reactors over fission reactors?

Why is iron the most abundant element in Earth’s core?

Compare the s- and r-processes in stellar nucleosynthesis.

What is the cosmic importance of unstable ${}^{\mathbf{\text{8}}}\mathbf{\text{Be}}$?

The reaction that will probably power the first commercial fusion reactor is

${}_{\mathbf{\text{1}}}{}^{\mathbf{\text{3}}}{\mathbf{\text{H + }}}_{\mathbf{\text{1}}}^{\mathbf{\text{2}}}\mathbf{\text{H}}{\mathbf{\to }}_{\mathbf{\text{2}}}^{\mathbf{\text{4}}}{\mathbf{\text{He + }}}_{\mathbf{\text{0}}}^{\mathbf{\text{1}}}\mathbf{\text{n}}$ 

How much energy would be produced per mole of reaction?

(Masses of atoms: ${}_{\mathbf{\text{1}}}{}^{\mathbf{\text{3}}}\mathbf{\text{H = 3.01605amu;}}_{\mathbf{\text{1}}}^{\mathbf{\text{2}}}\mathbf{\text{H = 2.0140amu}}$;

${}_{\mathbf{\text{2}}}{}^{\mathbf{\text{4}}}\mathbf{\text{He = 4.00260 amu;mass of }}_{\mathbf{\text{0}}}^{\mathbf{\text{1}}}\mathbf{\text{n = 1.008665 amu}}$ .)

The scene below depicts a neutron bombarding ${}^{\text{235}}\text{U}$ :

(b) Identify the other nuclide formed. 

(c) What is the most likely mode of decay of the nuclide with Z-55?

Which isotope in each pair is more stable? Why? 

(a) ${}_{\text{55}}{}^{\text{140}}\text{Cs}$or  ${}_{\text{55}}{}^{\text{133}}\text{Cs}$                              (b)${}_{\text{35}}{}^{\text{79}}\text{Br}$ or  ${}_{\text{35}}{}^{\text{78}}\text{Br}$

(c) ${}_{\text{12}}{}^{\text{28}}\text{Mg}$or ${}_{\text{12}}{}^{\text{24}}\text{Mg}$                                (d) ${}_{\text{7}}{}^{\text{14}}\text{N}$or ${}_{\text{7}}{}^{\text{18}}\text{N}$

A bone sample containing$strontium-90 \left(t_{1/2}=29yr\right)$  emits$7.0\times {10}^4{\beta }^{-}$  particles per month. How long will it take for the emission to decrease todata-custom-editor="chemistry" $1.0\times {10}^4$  particles per month?

The rd-century starship Enterprise uses a substance called “dilithium crystals” as its fuel. 

(a) Assuming this material is the result of fusion, what is the product of the fusion of two ${}^{6}Li$nuclei ?

(b) How much energy is released per kilogram of dilithium formed? (Mass of one ${}^{6}Li$ atom is 6.01512 amu.) 

(c) When four ${}^{1}H$ atoms fuse to form ${}^{4}He$, how many positrons are released? 

(d) To determine the energy potential of the fusion processes in parts (b) and (c), compare the changes in mass per kilogram of dilithium and of . 

(e) Compare the change in mass per kilogram in part (b) to that for the formation of ${}^{4}He$by the method used in current fusion reactors 

(f) Using early st-century fusion technology, how much tritium can be produced per kilogram of ${}^{6}Li$in the following reaction: ${}_3{}^{6}Li{+}_0^{1}n{\to }_2^{4}He{+}_1^{3}H$? When this amount of tritium is fused with deuterium, what is the change in mass? How does this quantity compare with the use of dilithium in part (b)?

What fraction of the  ${}^{235}U\left(t_{1/2}=7.0\times {10}^{8}yr\right)$ created when Earth was formed would remain after $2.8\times {10}^{9}yr$ ?

${}^{238}U\left(t_{1/2}=4.5\times {10}^{9}yr\right)$ begins a decay series that ultimately forms 206Pb . The scene below depicts the relative number of ${}^{238}U$  atoms (red) and ${}^{206} Pb$   atoms (green) in a mineral. If all the Pb comes from ${}^{238}U$ , calculate the age of the sample.

Technetium-99m is a metastable nuclide used in numerous cancer diagnostic and treatment programs. It is prepared just before use because it decays rapidly through y  emission:

 ${}^{99 m}T{\to }^{99}Tc+\gamma$

Use the data below to determine 

(a) The half-life of  ${}^{99 m}Tc$; 

(b) The percentage of the isotope that is lost if it takes 2.0 h to prepare and administer the dose.

How many curies are produced by 1.0 mol  of ? How many becquerels ${}^{40} K\left(t_{1/2}=\right.\left.1.25\times {10}^{9}yr\right)$?

The fraction of a radioactive isotope remaining at time t is${\left(\frac{1}{2}\right)}^{t/t_{1/2}}$ , where  $t_{1/2}$ is the half-life. If the half-life of carbon-14 is 5730yr , what fraction of carbon- 14 in a piece of charcoal remains after 

(a)  10.0yr; 

(b) $10.0\times {10}^{3}yr$ ; 

(c) $10.0\times {10}^{4}yr$ ? 

(d) Why is radiocarbon dating more reliable for the fraction remaining in part (b) than that in part (a) or in part (c)?

The isotopic mass of ${}_{86}{}^{210}Rn$  is 209.989669 . When this nuclide decays by electron capture, it emits  2.368MeV. What is the isotopic mass of the resulting nuclide?

Exactly 0.1 of the radioactive nuclei in a sample decay per hour. Thus, after n hours, the fraction of nuclei remaining is  (0.900)ⁿ. Find the value of n equal to one half-life.

In the 1950s, radioactive material was spread over the land from aboveground nuclear tests. A woman drinks some contaminated milk and ingests 0.500 g of ⁹⁰Sr, which is taken up by bones and teeth and not eliminated. 

(a) How much ${}^{90}Sr(t_{1/2}=29yr)$ is present in her body after 10yr ? 

(b) How long will it take for 99.9% of the ⁹⁰Sr  to decay?

The scene below represents a reaction (with neutrons grey and protons purple) that occurs during the lifetime of a star. 

(a) Write a balanced nuclear equation for the reaction. 

(b) If the mass difference is 7.7x10^-2, find the energy (kJ) released.

What volume of radon will be produced per hour at STP from 1.000 g of mass of ${}^{226}Ra(t_{1/2}=1599yr;1yr=8766h;$one ²²⁶Ra atom =226.025402 amu)

${}^{90}Kr(t_{1/2}=32s)$ is used to study respiration. How soon after being made must a sample be administered to the patient if the activity must be at least 90% of the original activity?

A decay series starts with the synthetic isotope ₉₂²³⁹U. The first four steps are emissions of a particle ${\beta }^{-}$, another ${\beta }^{-}$, an $\alpha$particle, and another $\alpha$. Write a balanced nuclear equation for each step. Which natural series could start by this sequence?

The overall reaction taking place during hydrogen burning in a young star is

 $4{ }_1^{1}H{\to }_2^{4}He+2{ }_1^0\beta +2 \nu +energy$

How much energy (in MeV) is released per He nucleus formed? Per mole of He? (Masses: ₁¹H  atom=1.007825 amu  ;  ⁴₂He atom-4.00260 amu  ; positron $-5.48580\times {10}^{-4}amu$.)