21: Nuclear Chemistry
- Page ID
- 316729
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Textbook: Section 21.2
Exercise \(\PageIndex{2.a}\)
Identify the missing element in isotopic notation:
a. \(_{53}^{138}\textrm{I}\rightarrow \textrm{?}+ _{-1}^{0}\textrm{e}\)
b. \(_{92}^{238}\textrm{U}\rightarrow \textrm{?}+ _{2}^{4}\textrm{He}\)
c. \(^{210}_{82}\textrm{Pb}\rightarrow \textrm{?}+ _{-1}^{0}\textrm{e}\)
d. \(^{1}_{0}\textrm{n}\rightarrow \textrm{?}+ ^{0}_{-1}\textrm{e}\)
e. \(^{238}_{92}\textrm{U}+^{1}_{0}\textrm{n}\rightarrow \textrm{?}+ ^{0}_{-1}\textrm{e}\)
f. \(^{239}_{94}\textrm{Pu}+_{2}^{4}\textrm{He}\rightarrow \textrm{?}+ ^{1}_{0}\textrm{n}\)
g. \(^{235}_{92}\textrm{U}+2 ^{1}_{0}\textrm{n}\rightarrow \textrm{?}+ ^{90}_{38}\textrm{Sr}+^{1}_{0}\textrm{n}\)
h. \(^{238}_{92}\textrm{U}+\textrm{?} \rightarrow + 6^{1}_{0}\textrm{n}+^{244}_{98}\textrm{Cf}\)
- Answer a
-
\(_{53}^{138}\textrm{I}\rightarrow _{54}^{138}\textrm{Xe}+ _{-1}^{0}\textrm{e}\)
- Answer b
-
\(^{238}_{92}\textrm{U}\rightarrow ^{234}_{90}\textrm{Th}+ ^{4}_{2}\textrm{He}\)
- Answer c
-
\(^{210}_{82}\textrm{Pb}\rightarrow ^{210}_{83}\textrm{Bi}+ _{-1}^{0}\textrm{e}\)
- Answer d
-
\(^{1}_{0}\textrm{n}\rightarrow + ^{1}_{1}\textrm{H}+^{0}_{-1}\textrm{e}\)
- Answer e
-
\(^{238}_{92}\textrm{U}+^{1}_{0}\textrm{n}\rightarrow ^{239}_{93}\textrm{Np}+ ^{0}_{-1}\textrm{e}\)
- Answer f
-
\(^{239}_{94}\textrm{Pu}+_{2}^{4}\textrm{He}\rightarrow ^{242}_{96}\textrm{Cm}+ ^{1}_{0}\textrm{n}\)
- Answer g
-
\(^{235}_{92}\textrm{U}+2 ^{1}_{0}\textrm{n}\rightarrow ^{146}_{54}\textrm{Xe}+ ^{90}_{38}\textrm{Sr}+^{1}_{0}\textrm{n}\)
- Answer h
-
\(^{238}_{92}\textrm{U}+^{12}_{6}\textrm{C}\rightarrow + 6^{1}_{0}\textrm{n}+^{244}_{98}\textrm{Cf}\)
21.4: Rates of Radioactive Decay
Textbook: Section 21.4
Exercise \(\PageIndex{4.a}\)
How many grams of 238U are left after 40.0 years if a sample originally weighed 150. grams and had a half life of 4.5x108 years?
- Answer
-
N0=150g
t1/2=4.5x108 years
t=40.0 years
\(\textrm{N}=\textrm{N}_{0}\left ( \frac{1}{2} \right )^{\frac{t}{t_{1/2}}}\\
\textrm{N}=150g\left ( \frac{1}{2} \right )^{\frac{40.0 years}{4.5x10^{8}years}}\)N=149.999999
150g of 238U are left after 40 years
Exercise \(\PageIndex{4.b}\)
How many grams of 137Cs are left after 28 years if a sample originally weighed 75 grams and had a half life of 30 years?
- Answer
-
N0=75g
t1/2=30 years
t=28 years
\(\textrm{N}=\textrm{N}_{0}\left ( \frac{1}{2} \right )^{\frac{t}{t_{1/2}}}\\
\textrm{N}=75g\left ( \frac{1}{2} \right )^{\frac{28 years}{30 years}}\)N=39.3g
Exercise \(\PageIndex{4.c}\)
How many grams of 14C are left after 150 years if a sample originally weighed 16 grams and had a half life of 5715 years?
- Answer
-
N0=16g
t1/2=5715 years
t=150 years
\(\textrm{N}=\textrm{N}_{0}\left ( \frac{1}{2} \right )^{\frac{t}{t_{1/2}}}\\
\textrm{N}=16g\left ( \frac{1}{2} \right )^{\frac{150 years}{5715 years}}\)N=15.7g
Exercise \(\PageIndex{4.d}\)
How many grams of 40K are left after 1000 years if a sample originally weighed 45 grams and had a half life of 1.3x109 years?
- Answer
-
N0=45g
t1/2=1.3x109 years
t=1000 years
\(\textrm{N}=\textrm{N}_{0}\left ( \frac{1}{2} \right )^{\frac{t}{t_{1/2}}}\\
\textrm{N}=45g\left ( \frac{1}{2} \right )^{\frac{1000 years}{1.3x109 years}}\)N=45g
Exercise \(\PageIndex{4.e}\)
How many grams of 131I are left after 15 years if a sample originally weighed 25 grams and had a half life of 8.03 days?
- Answer
-
N0=25g
t1/2=8.03 days
t=15 years
\(\textrm{15 years} \times \frac{\textrm{365 days}}{\textrm{1 year}}=\textrm{5475 days}\)
\(\textrm{N}=\textrm{N}_{0}\left ( \frac{1}{2} \right )^{\frac{t}{t_{1/2}}}\\
\textrm{N}=25g\left ( \frac{1}{2} \right )^{\frac{5475 days}{8.03 days}}\)N=0 g