Question
From data presented in the first few paragraphs of Module $42-3,$ find (a) the disintegration constant $\lambda$ and (b) the half-life of ${ }^{238} \mathrm{U}$.
Step 1
It states that 1 gram of ${ }^{238} \mathrm{U}$ contains $2.5 \times 10^{21}$ atoms and that 12,000 atoms disintegrate per minute. a) Show more…
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The accompanying graph illustrates the decay of $_{42}^{88} \mathrm{Mo}$ which decays via positron emission. (a) What is the half-life of the decay? (b) What is the rate constant for the decay?(c) What fraction of the original sample of $_{42}^{88} \mathrm{Mo}$ remains after 12 $\mathrm{min}$ ? (d) What is the product of the decay process? [Section 21.4$]$
Show that the decay constant and half-life are related by $t_{1 / 2}=\ln 2 / \lambda=0.693 / \lambda$.
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