Question

Radium- 226 decays by emitting an alpha particle. What is the daughter nucleus? a) \(\mathrm{Rd}\) b) \(R n\) c) \(\mathrm{Bi}\) d) \(\mathrm{Pb}\)

Short answer

a) Ra b) Rn c) Pa d) U Answer: b) Rn

Step-by-step solution

Understand Alpha Decay and Alpha Particles

Alpha decay is a type of radioactive decay in which an unstable atomic nucleus emits an alpha particle. An alpha particle is a helium-4 nucleus, which consists of 2 protons and 2 neutrons. As an equation, an alpha particle can be represented as: \(_{2}^{4}\textrm{He}\).

Write the Nuclear Decay Equation

To find the daughter nucleus, we will need to write the nuclear decay equation for Radium-226 undergoing alpha decay. The general form for an alpha decay equation is: $$_{Z}^{A}X \rightarrow _{Z-2}^{A-4}Y + _{2}^{4}\textrm{He}$$ Where \(_Z^AX\) represents the parent nucleus (Radium-226 in this case), \(_{Z-2}^{A-4}Y\) represents the daughter nucleus, and \(_{2}^{4}\textrm{He}\) represents the alpha particle.

Fill Out the Decay Equation

Now, we need to fill in the information about Radium-226 in the decay equation. Radium is denoted by the symbol \(\textrm{Ra}\) and has an atomic number (protons) of 88, and its atomic mass (protons + neutrons) is 226, so it can be represented as: \(_{88}^{226}\textrm{Ra}\). Plugging this into the alpha decay equation, we get: $$ _{88}^{226}\textrm{Ra} \rightarrow _{Z-2}^{A-4}Y + _{2}^{4}\textrm{He} $$

Calculate the Atomic Number and Mass for the Daughter Nucleus

To find the daughter nucleus, we need to determine its atomic number (Z-2) and atomic mass (A-4). Since Radium-226 has an atomic number of 88, the daughter nucleus will have an atomic number of (88 - 2) = 86. And, since Radium-226 has an atomic mass of 226, the daughter nucleus will have an atomic mass of (226 - 4) = 222. So, the daughter nucleus can be represented as: \(_{86}^{222}Y\).

Identify the Daughter Nucleus

Finally, we need to identify the element with atomic number 86 to determine the daughter nucleus. From the periodic table, we can see that the element with atomic number 86 is Radon (Rn). Therefore, the daughter nucleus is: \(_{86}^{222}\textrm{Rn}\). Given the choices in the exercise, the correct answer is (b) \(Rn\).