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?

Short answer

The stable nucleus formed after Radon-222 undergoes three alpha emissions and two beta emissions is Lead-210 (Pb-210), with 82 protons and 128 neutrons.

Step-by-step solution

Understanding Alpha and Beta Emissions

In an alpha emission, an unstable nucleus loses two protons and two neutrons, resulting in the emission of an alpha particle. In the case of beta emissions, a neutron is converted to a proton, and an electron (beta particle) is released.

Identify Radon-222's Protons and Neutrons

Radon has an atomic number of 86, so Radon-222 has 86 protons and 222 - 86 = 136 neutrons.

Calculate the changes due to Alpha Emissions

There are three alpha emissions, and in each emission, two protons and two neutrons are lost. So, a total of 6 protons and 6 neutrons are lost. After these emissions, the nucleus has 80 protons (86 - 6) and 130 neutrons (136 - 6).

Calculate the changes due to Beta Emissions

There are two beta emissions, and in each emission, a neutron converts into a proton. So, the nucleus gains 2 protons and loses 2 neutrons. The total number of protons becomes 82 (80 + 2) and the number of neutrons becomes 128 (130 - 2).

Identify the Stable Nucleus

The stable nucleus formed has 82 protons and 128 neutrons. The element with an atomic number of 82 is lead (Pb). Therefore, the stable nucleus formed is Lead-210 (Pb-210).