Problem 16 - Chemistry: The Central Science in SI Units, Global Edition

Question

What particle is produced during the following decay processes: (a) actinium-215 decays to francium-211; (b) boron- 13 decays to carbon-13; (c) holmium-151 decays to terbium- \(147 ;\) (d) carbon-11 decays to boron-11?

Step-by-Step Solution

Answer

The particles produced during the decay processes are: (a) an alpha particle; (b) an electron; (c) an alpha particle; (d) a positron.

Step 1: a) Actinium-215 decays to Francium-211

We see that a change in atomic number from 89 (Actinium) to 87 (Francium) has taken place, which indicates that Ac-215 has undergone alpha decay. An alpha particle consists of 2 protons and 2 neutrons, so the produced particle is an alpha particle. The decay equation is: \[Ac-215 \rightarrow Fr-211 + \alpha\]

Step 2: b) Boron-13 decays to Carbon-13

The change in atomic number from 5 (Boron) to 6 (Carbon) means 1 neutron has been converted into 1 proton, which indicates B-13 has undergone beta-minus decay. The produced particle is an electron. The decay equation is: \[B-13 \rightarrow C-13 + \beta^-\]

Step 3: c) Holmium-151 decays to Terbium-147

There is a change in atomic number from 67 (Holmium) to 65 (Terbium), which indicates that Ho-151 has undergone alpha decay. An alpha particle consists of 2 protons and 2 neutrons, so the produced particle is an alpha particle. The decay equation is: \[Ho-151 \rightarrow Tb-147 + \alpha\]

Step 4: d) Carbon-11 decays to Boron-11

The change in atomic number from 6 (Carbon) to 5 (Boron) suggests that 1 proton has been converted into 1 neutron, which indicates that C-11 has undergone beta-plus decay. The produced particle is a positron. The decay equation is: \[C-11 \rightarrow B-11 + \beta^+\] So the particles produced during each decay process are: a) an alpha particle b) an electron c) an alpha particle d) a positron

Key Concepts

Alpha Decay

Alpha decay is a type of nuclear decay where the decay parent emits an alpha particle. An alpha particle consists of 2 protons and 2 neutrons, essentially a helium nucleus. During this process, the atomic number of the element decreases by 2, and the mass number decreases by 4.This means the original element loses two protons and two neutrons:

• The atomic number goes down, indicating a move to a new element on the periodic table.
• The mass number decreases, reflecting the loss of nuclear particles.

An example would be actinium-215 decaying to francium-211, where an alpha particle (\[\alpha\]) is emitted, moving from Actinium (89 protons) to Francium (87 protons). Alpha decay often occurs in heavier elements where the electrostatic forces between protons are significant, and the nucleus needs to become more stable.

Beta-Minus Decay

Beta-minus decay occurs when a neutron in the nucleus transforms into a proton, emitting a beta particle. A beta particle is an electron (\[ \beta^- \]) that is ejected from the nucleus. This process results in:

• The increase of the atomic number by 1, as a neutron becomes a proton.
• No change in the mass number, as electrons and protons are nearly the same in terms of mass contributions.

For instance, in the decay of boron-13 to carbon-13, a neutron changes into a proton, increasing the atomic number from 5 to 6. The emitted electron helps balance the change in charge. Beta-minus decay is common in isotopes where there's an excess of neutrons.

Beta-Plus Decay

Beta-plus decay, also known as positron emission, happens when a proton converts into a neutron while emitting a positron (\[ \beta^+ \]).A positron is the antimatter counterpart of an electron, carrying a positive charge:

• The atomic number decreases by 1 because a proton changes to a neutron.
• The mass number remains the same since neutrons and protons contribute similarly to mass.

This decay process is observed in carbon-11 decaying to boron-11. Here the atomic number decreases from 6 to 5 as a positron is emitted. Beta-plus decay assists in balancing the neutron-proton ratio in isotopes where there are too many protons.

Particles Produced in Decay

During nuclear decay, specific particles are produced depending on the type of decay:

• **Alpha particles** (\[ \alpha \]): Consisting of 2 protons and 2 neutrons, they are emitted during alpha decay, reducing both atomic and mass numbers.
• **Beta particles** (\[ \beta^- \]): These electrons result from beta-minus decay when a neutron turns into a proton, increasing the atomic number.
• **Positrons** (\[ \beta^+ \]): Produced in beta-plus decay, these positively charged particles result from a proton converting into a neutron, decreasing the atomic number.

Understanding these particles and the decay processes allows for insights into elemental transformations and stability within nuclei. This knowledge is crucial for applications ranging from medical diagnostics to energy production.