Question

Francium-223 decays to polonium-215 via three decay steps. Propose a possible three-step sequence for the overall process.

Short answer

A possible three-step decay sequence for Francium-223 to Polonium-215 can be two successive alpha decays followed by a beta decay. The sequence is: Alpha decay of Francium-223 to element with atomic number 85 and mass number 219, another alpha decay to element with atomic number 83 and mass number 215, followed by beta decay to Polonium-215.

Step-by-step solution

Identify the Overall Decay Process

Determine the atomic numbers and mass numbers of Francium-223 and Polonium-215 to understand the overall decay process. Francium (Fr) has an atomic number of 87 and a mass number of 223. Polonium (Po) has an atomic number of 84 and a mass number of 215. The overall decay process involves a decrease of 3 in atomic number and 8 in mass number.

First Decay Step

The first decay step could be an alpha decay, where the unstable nucleus emits an alpha particle composed of 2 protons and 2 neutrons. This results in a decrease of 2 in the atomic number and 4 in the mass number. If Francium-223 goes through an alpha decay, the new element will have an atomic number of 85 and a mass number of 219.

Second Decay Step

The second decay step could again be an alpha decay. If the new element with atomic number 85 and mass number 219 also emits an alpha particle, the daughter nucleus will now have an atomic number of 83 and a mass number of 215.

Third Decay Step

The third decay step must be a beta decay to increase the atomic number by one without changing the mass number. In beta decay, a neutron is transformed into a proton and emits an electron (beta particle). The element with atomic number 83 and mass number 215 will transform into Polonium (atomic number 84) with the same mass number.

Key concepts

Alpha Decay Process

The alpha decay process is a common mode of radioactive decay in which an unstable nucleus ejects an alpha particle. An alpha particle is essentially a helium nucleus, consisting of two protons and two neutrons. When an atom undergoes alpha decay, its mass number decreases by 4 due to the loss of these four nucleons, and its atomic number decreases by 2 as a result of losing two protons, thus changing the element to another further up the periodic table.

For example, in the decay of Francium-223, which has an atomic number of 87, the emission of an alpha particle would result in an element with an atomic number of 85. The mass number would correspondingly decrease from 223 to 219. This transformation can be represented by the equation:\[ \text{Fr}^{223}_{87} \rightarrow \text{He}^{4}_{2} + \text{X}^{219}_{85} \]
Here, the 'X' indicates the new element formed as a result of alpha decay. A real example of an alpha emitter is Uranium-238 decaying into Thorium-234.

Beta Decay Process

The beta decay process involves the transformation of a neutron into a proton within the nucleus of an atom, which increases the atomic number by 1 while keeping the mass number unchanged. During beta decay, three particles are released: a beta particle (which is an electron), an antineutrino, and a proton that remains in the nucleus. The nucleus's charge increases by one because of the additional proton, but the mass remains virtually the same because the electron's mass is negligible compared to that of a neutron or proton.

In the given exercise, following two alpha decays, the element with an atomic number of 83 and a mass number of 215 undergoes beta decay. The decay can be represented as:\[ \text{X}^{215}_{83} \rightarrow \text{e}^- + \text{Y}^{215}_{84} \]In this equation, 'X' is the hypothetical element before beta decay occurs, and 'Y' represents Polonium (Po), the new element formed after the decay. The electron, \text{e}^-, is the beta particle ejected from the nucleus.

Atomic Number and Mass Number

The atomic number and mass number are fundamental to understanding chemical elements and their isotopes. The atomic number, denoted as 'Z', represents the number of protons in an atom's nucleus and uniquely identifies the element. The mass number, denoted as 'A', is the total number of protons and neutrons in the nucleus. For instance, Francium-223 has an atomic number (Z) of 87 and a mass number (A) of 223.

When considering radioactive decay sequences, changes to these numbers can indicate the type of decay occurring:

• Alpha decay decreases the mass number by 4 and the atomic number by 2.
• Beta decay keeps the mass number constant but increases the atomic number by 1.

As such, by observing the change in atomic and mass numbers during a sequence of decays, we can trace the path from the parent isotope to the daughter product. The sequence described in the exercise shows a clear example of how these numbers change step by step as Francium-223 undergoes a series of decays to become Polonium-215.