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The barium isotope ¹³¹Ba has a half-life of 12 days. A 250 $\mathrm{μ}$mg

sample of ¹³¹Ba is prepared. What is the mass of ¹³¹Ba after

(a) 1 day, (b) 10 days, and (c) 100 days?

The radium isotope ²²⁶Ra has a half-life of 1600 years. A

sample begins with 1.00x10^{10 226}Ra atoms. How many are left

after (a) 200 years, (b) 2000 years, and (c) 20,000 years?

How many protons and how many neutrons are in$\text{(a)}{}^6\mathrm{Li},\text{(b)}{}^{54}\mathrm{Cr}\text{, (c)}{}^{54}\mathrm{Fe}\text{, and (d)}{}^{220}\mathrm{Rn}\text{?}$

a. Is the binding energy of a nucleus with $A=200$more than, less than, or equal to the binding energy of a nucleus with $A=60$? Explain.

b. Is a nucleus with $A=200$more tightly bound, less tightly bound, or bound equally tightly as a nucleus with $A=60$? Explain.

A sample of 1.0x10¹⁰atoms that decay by alpha emission

has a half-life of 100 min. How many alpha particles are emitted

between t = 50 min and t = 200 min?

The radioactive hydrogen isotope ³H, called tritium, has a

half-life of 12 years.

a. What are the decay mode and the daughter nucleus of tritium?

b. What are the lifetime and the decay rate of tritium?

What is the half-life in days of a radioactive sample with 5.0 x 10¹⁵

atoms and an activity of 5.0 x 10⁸ Bq?

The half-life of ⁶⁰Co is 5.27 years. The activity of a ⁶⁰Co

sample is 3.50 x 10⁹ Bq. What is the mass of the sample?

Identify the unknown isotope X in the following decays.

$$\begin{gathered} \text{a.}\mathrm{X}→{}^{224}\mathrm{Ra}+\mathrm{Î\pm } \\ \text{b.}{}^{35}\mathrm{S}→\mathrm{X}+{\mathrm{e}}^{-}+\stackrel{¯}{\mathrm{ν}} \\ \text{c.}\mathrm{X}→{}^{40}\mathrm{K}+{\mathrm{e}}^{+}+\mathrm{ν} \\ \text{d.}{}^{24}\mathrm{Na}→{}^{24}\mathrm{Mg}+{\mathrm{e}}^{-}+\stackrel{¯}{\mathrm{ν}}→\mathrm{X}+\mathrm{γ} \end{gathered}$$

Identify the unknown isotope X in the following decays.

$$\begin{gathered} \text{a.}{}^{230}\mathrm{Th}→\mathrm{X}+\mathrm{Î\pm } \\ \text{b.}{}^{35}\mathrm{S}→\mathrm{X}+{\mathrm{e}}^{-}+\stackrel{¯}{\mathrm{ν}} \\ \text{c.}\mathrm{X}→{}^{40}\mathrm{K}+{\mathrm{e}}^{+}+\mathrm{ν} \\ \text{d.}{}^{24}\mathrm{Na}→{}^{24}\mathrm{Mg}+{\mathrm{e}}^{-}+\stackrel{¯}{\mathrm{ν}}→\mathrm{X}+\mathrm{γ} \end{gathered}$$