Under certain circumstances, a nucleus can decay by emitting a particle more massive than an `alpha`-particle. Consider the following decay processes:
`._(88)Ra^(223)to._(82)Pb^(209)+._(6)C^(14)`, `._(88)Ra^(223)to._(86)Rn^(219)+._(2)He^(4)`
(a) Calculate the Q-values for these decays and determine that both are energetically allowed.

Explanation

To solve the problem, we need to calculate the Q-values for the two decay processes and determine if they are energetically allowed. The Q-value is calculated using the mass defect, which is the difference in mass between the original nucleus and the products after decay.

### Step-by-Step Solution:

#### Step 1: Calculate the Q-value for the first decay process
The first decay process is:
\[
_{88}^{223}\text{Ra} \rightarrow _{82}^{209}\text{Pb} + _{6}^{14}\text{C}
...