Chapter 10: Problem 49

Write the complete decay equation in the complete \(_{Z}^{A} \mathrm{X}_{N}\) notation for the beta \(\left(\beta^{-}\right)\) decay of \(^{3} \mathrm{H}\) (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs.

Short Answer

Expert verified

\[ _{1}^{3}\mathrm{H}_{2} \rightarrow _{2}^{3}\mathrm{He}_{1} + \beta^{-} + \bar{\nu} \]

Step by step solution

Identify tritium's atomic number and mass number

Tritium (\(^3\mathrm{H}\)) is an isotope of hydrogen. Hydrogen has an atomic number (Z) of 1. The mass number (A) of tritium is given as 3. So, tritium can be written as \(_{1}^{3}\mathrm{H}_{2}\), where N (number of neutrons) is 2.

Determine the resulting isotope after beta decay

In beta decay, a neutron converts into a proton. This increases the atomic number by 1 while keeping the mass number constant. For tritium, the atomic number will increase from 1 to 2. This new atomic number corresponds to the element helium. Since the mass number remains constant at 3, the resulting isotope after beta decay is \(_{2}^{3}\mathrm{He}_{1}\).

Write the complete decay equation

Now, we can write the decay equation using the \(_{Z}^{A}\mathrm{X}_{N}\) notation. The initial element is tritium \(_{1}^{3}\mathrm{H}_{2}\), and the resulting element is \(_{2}^{3}\mathrm{He}_{1}\). Since a high-energy electron (beta particle, \(\beta^{-}\)) and an antineutrino (\(\bar{\nu}\)) are released during the decay, we can include them in the equation. The complete decay equation is: \[ _{1}^{3}\mathrm{H}_{2} \rightarrow _{2}^{3}\mathrm{He}_{1} + \beta^{-} + \bar{\nu} \] This is the desired decay equation for the beta decay of tritium in the \(_{Z}^{A}\mathrm{X}_{N}\) notation.

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Write the complete decay equation in the complete \(_{Z}^{A} \mathrm{X}_{N}\) notation for the beta \(\left(\beta^{-}\right)\) decay of \(^{3} \mathrm{H}\) (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs.

Short Answer

Step by step solution

Identify tritium's atomic number and mass number

Determine the resulting isotope after beta decay

Write the complete decay equation

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