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Chemistry LibreTexts

21: Nuclear Chemistry

  • Page ID
    316729
  • 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

    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

     

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