Problem 72 - Chemistry: The Central Science

Question

Radon-222 decays to a stable nucleus by a series of three alpha emissions and two beta emissions. What is the stable nucleus that is formed?

Step-by-Step Solution

Answer

The stable nucleus formed after Radon-222 decays through three alpha emissions and two beta emissions is Lead-210 (Pb-210).

Step 1: Understanding Alpha and Beta Emissions

Alpha emission occurs when an unstable nucleus releases an alpha particle, which consists of 2 protons and 2 neutrons. This results in a decrease in the atomic number by 2 and a decrease in the mass number by 4. Beta emission occurs when an unstable nucleus releases a beta particle, which is an electron resulting from the conversion of a neutron to a proton. This leads to an increase in the atomic number by 1 and no change in the mass number. Now let's analyze the decay of Radon-222.

Step 2: Find the atomic number and mass number for Radon

Radon has an atomic number of 86 (which denotes the number of protons) and a mass number of 222 (which denotes the sum of protons and neutrons). So, initially, we have: Atomic Number: 86 Mass Number: 222

Step 3: Identify changes after three alpha emissions

After three alpha emissions, the Radon nucleus will lose 6 protons (2 protons per alpha emission) and 12 neutrons (4 total nucleons per alpha emission). Therefore, the changes in atomic number and mass number are: Atomic Number: 86 - 6 = 80 Mass Number: 222 - 12 = 210

Step 4: Identify changes after two beta emissions

After two beta emissions, the nucleus will gain 2 protons (1 proton per beta emission) and have no change in the number of neutrons. Therefore, the changes in atomic number and mass number are: Atomic Number: 80 + 2 = 82 Mass Number: 210 (no change)

Step 5: Determine the stable nucleus

Now that we have found the updated atomic number and mass number after all the emissions, we can determine the resulting stable nucleus. An element with an atomic number of 82 is lead (Pb), so the stable nucleus is: Lead-210 (Pb-210) Thus, the stable nucleus formed after Radon-222 decays through three alpha emissions and two beta emissions is Lead-210 (Pb-210).