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Which phrase describes the decay modes and the half-lives of K-37 and K-42?


(1) the same decay mode but different half-lives

(2) the same decay mode and the same half-life

(3) different decay modes and different half-lives

(4) different decay modes but the same half-life

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Among the choices the phrase describes the decay modes and the half-lives of K-37 and K-42 is different decay modes and different half-lives

Answer: (3) different decay modes and different half-lives

Explanation: Potassium-37 and Potassium-42 have the same number of protons  but different numbers of neutrons i.e. they have same atomic number but different mass number. They are isotopes. Thus K-37 and K-42 have different decay modes

K-37 is positron decay and K-42 is beta decay.

\(_{19}^{37}{\textrm {Kr}}\rightarrow _{18}^{37}{\textrm {Ar}}+_{+1}^0{\textrm {e}}\)

\(_{19}^{42}{\textrm {Kr}}\rightarrow _{20}^{42}{\textrm {Ca}}+_{-1}^0{\textrm {e}}\)


K-37 has a half life of 1.23 seconds and K-42 has a half life of 12.4 hrs.

Thus they have different decay modes and different half lives.

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