Question

If a radioactive isotope of thorium (atomic number 90 , mass number 232) emits 6 alpha particles and 4 beta particles during the course of radioactive decay, what are the atomic number and mass number of the stable daughter product?

Short answer

The daughter product is Lead (Pb) with atomic number 82 and mass number 208.

Step-by-step solution

Understanding Alpha Decay

Each alpha particle emission decreases the atomic number by 2 and the mass number by 4 because an alpha particle consists of 2 protons and 2 neutrons. Since 6 alpha particles are emitted, we calculate the changes as follows: Decrease in atomic number = 6 alpha particles × 2 = 12. Decrease in mass number = 6 alpha particles × 4 = 24.

Change in Atomic and Mass Numbers due to Alpha Decay

The original atomic number is 90, and the original mass number is 232. After emitting 6 alpha particles: New atomic number = 90 - 12 = 78. New mass number = 232 - 24 = 208.

Understanding Beta Decay

Each beta particle emission increases the atomic number by 1 because a neutron is converted into a proton, but the mass number remains unchanged. Since 4 beta particles are emitted, increase in atomic number = 4 beta particles × 1 = 4.

Adjustment of Atomic Number due to Beta Decay

The atomic number after alpha decay is 78. After emitting 4 beta particles, the new atomic number = 78 + 4 = 82. The mass number remains 208 as beta decay does not change the mass number.

Identifying the Daughter Element

The atomic number 82 corresponds to Lead (Pb) on the periodic table. Therefore, the stable daughter product is Lead with a mass number of 208.

Key concepts

Alpha Decay

Radioactive decay is a process by which an unstable atomic nucleus loses energy. In the case of alpha decay, this occurs by emitting an alpha particle. An alpha particle is made up of 2 protons and 2 neutrons. When a nucleus emits an alpha particle, its atomic number, which is the number of protons, decreases by 2. Additionally, the mass number, which is the total number of protons and neutrons in the nucleus, decreases by 4. This change occurs because the escape of the 2 protons and 2 neutrons from the nucleus reduces both counts by those same amounts. When observing changes due to alpha decay:

• Atomic number decrease: 2 units per alpha particle
• Mass number decrease: 4 units per alpha particle

This emission causes the element to move down two places on the periodic table, leading to the formation of a different element altogether.

Beta Decay

Beta decay is another form of radioactive decay, but it affects the atomic number differently than alpha decay. During beta decay, a neutron in the atomic nucleus is transformed into a proton. This process releases a beta particle, which is essentially an electron. As a result of this neutron-to-proton conversion, the atomic number increases by 1. This increase occurs because the number of protons in the nucleus has increased by one, moving the element one place higher on the periodic table. However, the mass number, which is the sum of protons and neutrons, stays the same because the change is an internal conversion of neutron to proton without the loss of nuclear mass. Important notes on beta decay:

• Atomic number increase: 1 unit per beta particle
• Mass number change: No change

This type of decay changes the identity of the element by altering its position in the periodic table, but without an impact on its overall mass.

Mass Number

The mass number is a fundamental property of an atom that is crucial in understanding atomic structure and nuclear chemistry. It represents the total number of protons and neutrons present in the nucleus of an atom. Neutrons have no charge, but they contribute significantly to the mass of the atom. As a result: - The mass number = number of protons + number of neutrons Changes in the mass number during radioactive processes like alpha decay are notable since each alpha particle emission reduces the mass number by 4. However, in beta decay, the mass number remains unchanged because only internal conversions are happening without any loss of particles from the atom's nucleus. Understanding mass number is essential for identifying isotopes of elements and predicting outcomes of radioactive decay processes, as isotopes are atoms of the same element (same number of protons) but with different numbers of neutrons.

Atomic Number

The atomic number of an element is a critical identifier for every chemical element on the periodic table. It defines the number of protons in the nucleus of an atom. Since protons are positively charged particles, the atomic number not only indicates the number of protons but also determines the element's electric charge balance when in a neutral state. The atomic number is crucial because:

• It defines the identity of the element
• It is the same as the number of electrons in a neutral atom, which balance the positive charge of the protons

During radioactive decay, changes to the atomic number are important indicators of transformation: - In alpha decay, the atomic number decreases by 2, changing the element to another with two fewer protons. - In beta decay, the atomic number increases by 1 as a neutron is converted to a proton, changing the element to one with one more proton. These changes crucially impact which element the atom will become in the decay process.