Chapter 19: Problem 18

In each pair of isotopes shown, indicate which one you would expect to be radioactive: (a) \({ }_{10}^{20} \mathrm{Ne}\) and \({ }_{10}^{17} \mathrm{Ne},(\mathrm{b}){ }_{20}^{40} \mathrm{Ca}\) and \({ }_{20}^{45} \mathrm{Ca},\) (c) \({ }_{42}^{95} \mathrm{Mo}\) and \({ }_{43}^{92} \mathrm{Tc},\) (d) \({ }_{80}^{195} \mathrm{Hg}\) and \({ }_{80}^{196} \mathrm{Hg},\) (e) \({ }_{83}^{209} \mathrm{Bi}\) and \({ }_{96}^{242} \mathrm{Cm}\)

Short Answer

Expert verified

The isotopes likely to be radioactive in each pair are \( {}_{10}^{17}Ne \), \( {}_{20}^{45}Ca \), \( {}_{43}^{92}Tc \), \( {}_{80}^{196}Hg \), and \( {}_{96}^{242}Cm \).

Step by step solution

Determine the isotope of each element likely to be radioactive

An atom is more inclined to be radioactive if it does not have an atomic number or mass number that aligns with the 'magic numbers'. Starting with (a), compare each pair and decide which doesn't satisfy the 'magic numbers' criterion: a) \( {}_{10}^{20}Ne \) and \( {}_{10}^{17}Ne \), b) \( {}_{20}^{40}Ca \) and \( {}_{20}^{45}Ca \), c) \( {}_{42}^{95}Mo \) and \( {}_{43}^{92}Tc \), d) \( {}_{80}^{195}Hg \) and \( {}_{80}^{196}Hg \), e) \( {}_{83}^{209}Bi \) and \( {}_{96}^{242}Cm \).

Result

Following the criterion, we can expect the following isotopes to be radioactive: a) \( {}_{10}^{17}Ne \), b) \( {}_{20}^{45}Ca \), c) \( {}_{43}^{92}Tc \), d) \( {}_{80}^{196}Hg \), e) \( {}_{96}^{242}Cm \). These isotopes have either atomic or mass numbers that are far from the 'magic numbers'.

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Step by step solution

Determine the isotope of each element likely to be radioactive

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