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Chapter 40: Problem 27

Write down equations to describe the \(\beta^{-}\) -decay of the following atoms: a) \({ }^{60} \mathrm{Co}\) b) \({ }^{3} \mathrm{H}\) c) \({ }^{14} \mathrm{C}\)

Short Answer

Expert verified
Question: Write down the equations for β− decay of Cobalt-60, Tritium, and Carbon-14. Answer: a) Cobalt-60: ${ }^{60}\mathrm{Co} \rightarrow { }^{60}\mathrm{Ni} + e^{-} + \bar{\nu_e}$ b) Tritium: ${ }^{3}\mathrm{H} \rightarrow { }^{3}\mathrm{He} + e^{-} + \bar{\nu_e}$ c) Carbon-14: ${ }^{14}\mathrm{C} \rightarrow { }^{14}\mathrm{N} + e^{-} + \bar{\nu_e}$

Step by step solution

01

Write the general equation for \(\beta^{-}\) decay

To begin with, we need to write a general equation for \(\beta^{-}\) decay. In this decay, a neutron (n) transforms into a proton (p), emitting an electron (e) and an electron-antineutrino (\(\bar{\nu}_e\)) in the process. This can be represented as: n \(\rightarrow\) p + e\(^{-}\) + \(\bar{\nu}_e\)
02

Write the provided isotopes in the form A ZX

In order to write the decay equations, we need first to express the given isotopes using the standard notation A ZX, where A is the mass number, Z is the atomic number, and X is the element symbol. a) \({ }^{60} \mathrm{Co}\) (Cobalt-60) b) \({ }^{3} \mathrm{H}\) (Tritium or Hydrogen-3) c) \({ }^{14} \mathrm{C}\) (Carbon-14)
03

Write the decay equations for each isotope

Now, we will write the decay equations for each isotope, applying the conservation of mass number and atomic number: a) \({ }^{60} \mathrm{Co}\) \(\rightarrow\) \({ }^{60} \mathrm{Ni}\) + e\(^{-}\) + \(\bar{\nu}_e\) b) \({ }^{3} \mathrm{H}\) \(\rightarrow\) \({ }^{3} \mathrm{He}\) + e\(^{-}\) + \(\bar{\nu}_e\) c) \({ }^{14} \mathrm{C}\) \(\rightarrow\) \({ }^{14} \mathrm{N}\) + e\(^{-}\) + \(\bar{\nu}_e\) These are the decay equations describing the \(\beta^{-}\) decay of Cobalt-60, Tritium, and Carbon-14.

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