21: Nuclear Chemistry

21.2: Nuclear Reactions

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

t_1/2=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

t_1/2=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

t_1/2=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

t_1/2=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

t_1/2=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