Question

A radioactive nucleus undergoes alpha decay, emitting an alpha particle (α) and resulting in the formation of a new nucleus. Consider the following information:

• The atomic number (Z) of the original nucleus is 92.
• The mass number (A) of the original nucleus is 238.
• The mass number (A) of the alpha particle is 4.
• The charge on the alpha particle is +2e, where e is the elementary charge.

Calculate the atomic number (Z) and the mass number (A) of the new nucleus formed after the alpha decay.

Answer

To calculate the atomic number (Z) of the new nucleus, we need to understand that during alpha decay, an alpha particle is emitted which contains two protons. Therefore, the atomic number (Z) of the new nucleus will be reduced by 2.

Hence, the atomic number (Z) of the new nucleus is 92 - 2 = 90.

To calculate the mass number (A) of the new nucleus, we need to understand that the mass number is the sum of protons and neutrons in the nucleus.

Given that the original nucleus has a mass number (A) of 238 and an alpha particle has a mass number (A) of 4, we can apply the conservation of mass number (A) during alpha decay.

The mass number (A) of the new nucleus will be the difference between the mass number (A) of the original nucleus and the mass number (A) of the emitted alpha particle.

Hence, the mass number (A) of the new nucleus is 238 - 4 = 234.

Therefore, the atomic number (Z) of the new nucleus is 90, and the mass number (A) of the new nucleus is 234.

Atomic number (Z) of the new nucleus = 92 - 2 = 90
Mass number (A) of the new nucleus = 238 - 4 = 234