Question 14.3: Complete the following equations with the correct particles ......
Complete the following equations with the correct particles and identify the mode of decay.
(a) { }_8^{15} O \rightarrow{ }_7^{15} N +\quad ?
(b) { }_{19}^{40} K \rightarrow ?+{ }_{-1}^0 \beta+\bar{\nu}
(c) { }_{19}^{40} K +? \rightarrow{ }_{18}^{40} Ar +\nu
Strategy As before, we rely on both mass numbers and charges to identify the missing species in the equations. Once each species has been identified, we can use our definitions of the various nuclear reactions to identify the reaction.
Consider each equation in turn.
(a) { }_8^{15} O \rightarrow{ }_7^{15} N + ?
There is no change in the mass number from oxygen- 15 to nitrogen- 15 , so the unknown particle has a mass number of zero. For the sum of the charges on the product side to equal eight, the unknown particle must have a charge of 1+. These two facts tell us that the unknown particle is a positron, and the event is positron emission. A neutrino is also needed to complete the equation.
{ }_8^{15} O \rightarrow{ }_7^{15} N +{ }_1^0 \beta+\nu
(b) { }_{19}^{40} K \rightarrow ? +{ }_{-1}^0 \beta+\bar{\nu}
We are looking at beta decay, so the mass number of the decaying isotope does not change. Thus the mass number of the product must be 40 . The sum of the charges of the products must be 19 , so the unknown must have a value of 20(19 = 20 – 1). The unknown is { }^{40} Ca, and the process is beta decay:
{ }_{19}^{40} K \rightarrow{ }_{20}^{40} Ca +{ }_{-1}^0 \beta+\bar{\nu}
(c) { }_{19}^{40} K +? \rightarrow{ }_{18}^{40} Ar +\nu
There is no change in mass number from potassium to argon in this reaction, so the mass number of the missing particle must be zero. For the sum of the charges of the reactants to equal 18 requires a charge of 1-. The missing particle is an electron, and the event is electron capture.
{ }_{19}^{40} K +{ }_{-1}^0 e \rightarrow{ }_{18}^{40} Ar +\nu
Discussion The examples here point out that it is not always easy to distinguish between various possible decay processes. We wrote the last equation as electron capture, for example, but { }_{19}^{40} K could also decay to { }_{18}^{40} Ar by positron emission.
{ }_{19}^{40} K \rightarrow{ }_{18}^{40} Ar +{ }_1^0 \beta+\nu
Also notice that in the last two equations, we have the same parent nucleus \left({ }_{19}^{40} K \right) decaying to two different daughter nuclei \left({ }_{20}^{40} Ca\right. and \left.{ }_{18}^{40} Ar \right). We’ve seen similar behavior in ordinary chemical reactions. Complete and incomplete combustion are one example in which the same reactants can produce different sets of products.
Check Your Understanding Carbon-11 is another unstable isotope of carbon. It decays by positron emission. Write the equation for this nuclear reaction.