5.E: Exercises
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Types of Radiation
Write the symbol for each of the following types of radiation:
a. Beta particle: __________
b. Alpha particle: __________
c. Gamma ray: __________
d. Neutron: __________
The type of radiation represented by the symbol \(\ce{^4_2He}\) is:
a. \(\alpha\) particle
b. \(\beta -\) particle
c. \(\beta +\) particle
d. \(\gamma\) ray
e. Heat ray
Identify the list with correct names of these particles or radiation types in the order listed: \(\ce{^1_1He, ^4_2He, ^0_{-1}\beta , ^0_0 \gamma}\)
a. proton, alpha particle, beta particle, gamma ray
b. alpha particle, neutron, gamma ray, \(\beta -\) particle
c. alpha particle, beta particle, gamma ray, positron
d. heat ray, alpha particle, beta particle, gamma ray
Which of the following statements about radiation is incorrect?
a. Both positrons and electrons have mass values of zero
b. Alpha particles have the shallowest tissue depth of the particles
c. Radioactive isotopes have stable nuclei
d. Gamma can travel farther than Alpha and Beta particles
e. Bruce Banner became the Hulk after being exposed to Gamma rays
Which of the following statements is true when a radioactive element undergoes beta decay?
a. The mass number of the new element stays the same, and the atomic number is decreased by 1.
b. The mass number of the new element stays the same, and the atomic number is increased by 1.
c. The mass number of the new element is decreased by 4, and the atomic number is decreased by 2.
d. The mass number of the new element stays the same, and the atomic number also stays the same.
(Matching) Match the following types of radiation with their appropriate symbol: \(\beta\), \(\gamma\), n, \(\beta^+\), \(\alpha\), p.
a. Alpha particle =
b. Beta particle =
c. Positron =
d. Gamma ray =
e. Proton =
f. Neutron =
What is the minimum required radiation protection for gamma radiation?
a. Lab coats
b. Nitrile gloves
c. Paper
d. Thick concrete
What is the minimum required radiation protection for beta particles?
a. Thick concrete
b. Paper
c. Lead
d. Lab coats
What is the minimum required radiation protection for alpha particles?
a. Lead
b. Paper
c. Lab coats
d. Heavy clothing
An alpha particle has two protons and four neutrons.
a. True
b. False
An alpha particle has two protons and two neutrons.
a. True
b. False
Identify and write the symbol for each of the following types of radiation:
a. contains two protons and two neutrons
b. has a mass number of 0 and a -1 charge
Nuclear Reactions
Yttrium-90 is a radioisotope used to treat liver cancer. Identify the missing part of the nuclear equation shown below for the decay of Yttrium-90.
\(^{90}_{39} \ce{Y} \ \rightarrow \ [ \ ] \ + \ ^{90}_{40} \ce{Zr}\)
a. \(\ce{^4_2 He}\)
b. \(\ce{^0_0 \gamma}\)
c. \(^0_{-1} e \)
d. \(^0_{+1} e \)
e. \( ^1_0 n \)
What is the radioactive particle released in the following nuclear equation?
\(^{90}_{38} \ce{Sr} \ \rightarrow \ ^{90}_{39} \ce{Y} \ + ?\)
a. Alpha particle
b. Beta particle
c. Gamma ray
d. Proton
e. Neutron
Americium-241 is a radioisotope used in smoke detectors. The isotope produces an electrical current that is disrupted by smoke, triggering an alarm. Identify the missing part of the nuclear equation shown below for the decay of Americium-241.
\(^{241}_{95} \ce{Am} \ \rightarrow \ ^{4}_{2} \ce{He} \ + \ [ \ ]\)
a. \(^{237}_{93} \ce{Am}\)
b. \(^{237}_{95} \ce{Am}\)
c. \(^{241}_{93} \ce{Np}\)
d. \(^{237}_{93} \ce{Np}\)
e. \(^{237}_{94} \ce{Pu}\)
What radioactive isotope is produced when a neutron bombards Cobalt-59 and releases an alpha particle?
Thorium-234 can be produced from the alpha decay of a heavier radioisotope, identify this heavier radioisotope.
Cerium-141 is a radioisotope used to assess blood flow through the heart.
a. What new radioisotope is produced when cerium-141 undergoes beta decay?
b. What new radioisotope is produced assuming that cerium-141 undergoes alpha decay?
The U.S. Environmental Protection Agency (EPA) estimates that radon (\(\ce{Rn}\)) causes about 20,000 lung cancer deaths in one year. What is the recommended maximum value of radiation that the level of \(\ce{Rn}\) should not exceed? Provide a relevant unit as well.
Determine the symbol of the new nucleus and complete the nuclear equation
a. \(^{214}_{84} \ce{Po} \ \rightarrow \ ^{210}_{82} \ce{Pb} \ + \ ? \)
b. \(^{213}_{83} \ce{Bi} \ \rightarrow \ ? \ + \ ^{4}_{2} \ce{He}\)
c. \(^{90}_{39} \ce{Y} \ \rightarrow \ ? \ + \ ^{0}_{-1} e \)
d. \(^{51}_{24} \ce{Cr} \ \rightarrow \ ? \ + \ ^{0}_{-1} e \)
e. \(^{64}_{29} \ce{Cu} \ \rightarrow \ ^{64}_{30} \ce{Zn} \ + \ ?\)
Radiation Measurements
Which of the following is not a unit used to measure radiation?
a. Millirem (mrem)
b. Radiation absorbed dose (rad)
c. Marie (Ma)
d. Curie (Ci)
e. Becquerel (Bq)
The isotope shown below is used for diagnostic imaging of the thyroid. If 80.0 mg of this isotope were prepared at 4:00 AM on Monday, how many mg remain at 6:00 AM on the following day (Tuesday)?
a. 80 mg
b. 40 mg
c. 20 mg
d. 10 mg
e. 15 mg
f. 26 mg
A technician in a nuclear laboratory was accidentally exposed to 5 mGy of radiation. How much was this technician exposed to in rad?
Estimate the amount of radiation absorbed by a 75.0 kg patient exposed to ionizing alpha radiation of 2.00 J. (1 rad = 0.01 J/kg)
a. 2.67 rad
b. 150 rad
c. 0.375 rad
d. 3750 rad
Which, if any, of the following statements about a Geiger counter is incorrect:
a. Uses ions from radiation to create an electrical signal as a means of detection
b. Detects gamma rays
c. Detects beta particles
d. All of the statements are correct
Two scientists John and Silas work under radiation susceptible condition. John works with up to 12 rad radiation and Silas works with up to 72 mGy radiation. Who works under more dangerous conditions? Note that 1 Gy = 100 rad.
The U.S. Food and Drug Administration (FDA) has approved the use of 0.3 to 1 kGy of radiation produced by coba for the treatment of foods. Which type nuclear reaction is used for this treatment?
a. Alpha decay
b. Beta decay
c. Positron emission
d. Gamma emission
Half-life of a Radioisotope
The longer the half-life of a radioactive isotope, the __________ dangerous it is.
a. More
b. Less
A chemistry student at GGC synthesized a new sulfonamide (S7) drug to help treat malaria. Using a spectrophotometer, the student observed that S7 converts to a colorless molecule in the presence of malaria parasite called Plasmodium falciparum. To study the rate of reaction, the student recorded the absorbance/amount of S7 at a wavelength of 570 nm. The results are summarized in the table below:
| Time (s) | Absorbance/Amount of S7 |
|---|---|
| 0 | 0.80 |
| 5 | 0.63 |
| 10 | 0.50 |
| 15 | 0.40 |
| 20 | 0.32 |
| 25 | 0.25 |
| 30 | 0.20 |
Determine the half-life of S7:
a. 5 s
b. 10 s
c. 15 s
d. 30 s
Arithmetic Question: Radium-223 dichloride (also called Xofigo) with a half-life of 11.4 days has been approved by the FDA to treat metastatic prostate cancer. Indicate the number of half-lives that has elapsed for a sample 34.2 days after application.
Radioisotope X has a half-life of 4.0 h. Based on the figure below, if the original sample of the radioisotope was 16.00 g, what percentage of the sample would be left after 12.0 hours?
a. 50.0%
b. 25.0%
c. 12.5%
d. 6.25%
e. 3.13%
The half-life of Strontium-85 is 65 days. How much of a 80. mg sample is left after 260 days?
24 g of an unknown radioactive substance decays to 1.5 g after 180 seconds. What is the half-life of this substance?
The radioactive decay of \(\ce{Cs}\)-137 is displayed in the plot below.
a. What is the half-life of this radioisotope? __________
b. An ancient lab purchased and stocked 176 g of \(\ce{Cs}\)-137, how many grams were left after 120 years? __________
c. What percent of the original sample is left after 60 years? __________
The table shown below lists half-lives of some radioisotopes.
| Element | Radioisotope | Half-Life | Type of Radiation |
|---|---|---|---|
| Naturally Occurring Radioisotopes | |||
| Carbon-14 | \(\ce{^{14}_6C}\) | 5730 yr | Beta |
| Potassium-40 | \(\ce{^{40}_{19}K}\) | \(1.3 \times 10^9\) yr | Beta, gamma |
| Radium-226 | \(\ce{^{226}_{88}Ra}\) | 1600 yr | Alpha |
| Strontium-90 | \(\ce{^{90}_{38}Sr}\) | 38.1 yr | Alpha |
| Uranium-238 | \(\ce{^{238}_{92}U}\) | \(4.5 \times 10^9\) yr | Alpha |
| Some Medical radioisotopes | |||
| Carbon-11 | \(\ce{^{11}_6C}\) | 20. min | Positron |
| Chromium-51 | \(\ce{^{51}_{24}Cr}\) | 28 days | Gamma |
| Iodine-131 | \(\ce{^{131}_{53}I}\) | 8.0 days | Gamma |
| Oxygen-15 | \(\ce{^{15}_8O}\) | 2.0 min | Positron |
| Iron-59 | \(\ce{^{50}_26Fe}\) | 44 days | Beta, gamma |
| Radon-222 | \(\ce{^{222}_{86}Rn}\) | 3.8 days | Alpha |
| Technetium-99m | \(\ce{^{99m}_{43}Tc}\) | 6.0 h | Gamma |
Which of the following properly describes the difference between the naturally occurring radioisotopes and the medical radioisotopes?
a. Naturally occurring radioisotopes are heavier elements than medical radioisotopes.
b. Naturally occurring radioisotopes have longer half-lives than medical radioisotopes.
c. Only naturally occurring radioisotopes emit alpha particles.
d. Only medical radioisotopes undergo gamma emission.
Use the graph below to answer the following questions.
a. How long is a half-life for carbon-14?
b. If only 25% of the carbon-14 remains, how old is the material containing the carbon-14?
c. If a sample originally had 120 atoms of carbon-14, how many atoms will remain after 16,110 years?
Use the graph below to answer the following questions. Assume one atom produces one count per minute.
a. How many atoms are in the original sample size of this radioisotope? __________
b. How long is the half-life? __________
c. How many atoms are left after 2 half-lives? __________
d. Approximately how many days would have to pass for there to be only 2.5 atoms of the sample remaining? __________. How many half-lives? __________
The following graph shows the radioactive decay curve for Iodine-131. This radioisotope is used in medicine to help diagnose issues with the thyroid such as cancer and hyperthyroidism. Use the graph to answer the following questions.
a. What percent of the isotope remains after 32 days? __________
b. What is the half-life of Iodine-131 in days? __________
c. A patient administered 20 mg of iodine-131. How many mg of this radioactive isotope will remain the body after 24 days? __________
Medical Applications of Radioactivity
Match the type of radiation (alpha, beta and gamma) with each of the following statements:
a. Does not penetrate skin
b. Lead and concrete used for shielding and protection
c. Higher ionizing potential and biological damage
Ionization radiation usually affects molecules in human cells like:
a. DNA
b. glucose
c. water
d. lipids
Which of the following radioisotopes will not be commonly used in the medical field?
a. Radium-226 (half-life = 1600 years)
b. Chromium-51 (half-life = 28 days)
c. Iodine-131 (half-life = 8.0 days)
d. Technetium-99m (half-life = 6.0 hours)
Fluorine-18 used in PET scans has a half-life of 110 min. If a 100.0 mg sample of the radioisotope is shipped at 8:00 a.m., and the scan requires a minimum of 12.5 mg, what is the latest arrival time possible?
a. 2:00 p.m.
b. 1:30 p.m.
c. 1:00 p.m.
d. 12:30 p.m.
e. 12:00 p.m.
The following picture shows the penetrating power of radiation.
a. Which radiation (alpha, beta, or gamma) is most dangerous upon human exposure?
b. Which radiation (alpha, beta, or gamma) is most energetic?
Nuclear Fission and Fusion
Radiologists, in some cases, use bismuth-213 to treat cancer wherein its decay produces a high energy alpha particle that destroys cancer cells. What daughter radioisotope is produced when bismuth-213 undergoes decay? Thallium-209
View this link to see a simulation of nuclear fission, then answer the question. Identify each process as an example of nuclear fusion or nuclear fission:
a. A large nuclei splits into smaller nuclei
b. Smaller nuclei combine to form larger ones
c. Very high temperatures are attained
d. Cooling rods are used to control energy
e. A neutron slams into a heavy nuclei
f. Powers the sun and creates huge amounts of energy
When \(\ce{^{235}U}\) is bombarded with a single neutron, the following fission reaction occurs:
\( ^{235}_{x} \ce{U} \ + \ ^{1}_{y} n \ \rightarrow \ ^{141}_{56} \ce{Ba} \ + \ ^{92}_{36}\ce{Kr} +z ^1_y n\)
Find \(x\), \(y\) and \(z\)
a. \(x = 92\), \(y = 0\), \(z = 3\)
b. \(x = 93\), \(y = 1\), \(z = 3\)
c. \(x = 92\), \(y = 1\), \(z = 3\)
d. \(x = 93\), \(y = 0\), \(z = 2\)
Complete the following nuclear reaction equation.
\([ \ ] \ + \ ^{56}_{27} \ce{Co} \ \rightarrow \ ^{56}_{25} \ce{Mn} \ + \ ^4_2 \ce{He}\)
a. \(\ce{^4_2 He}\)
b. \(\ce{^0_0 \gamma}\)
c. \(^0_{-1} e \)
d. \(^0_{+1} e \)
e. \(^1_0 n \)
Nuclear energy production
__________ is the process of combining two light nuclei to form a heavier, more stable nucleus while __________ is the process of splitting a heavy nucleus into two lighter, more stable nuclei.
Current nuclear power plants employ controlled __________ to produce energy.
Our sun produces its energy through nuclear __________ of protons to form helium.
Nuclear reactions which occur successively and create a large number of high-energy neutrons are referred to as a __________ __________.