Question

When Bi-209 is bombarded with Ni-64, one neutron and a new isotope, \(\mathrm{X},\) are formed. The isotope then goes through a series of alpha particle emissions. (a) Write the nuclear symbol for the isotope formed. (b) Write the nuclear symbol for the isotope formed after the third alpha particle emission.

Short answer

Answer: (a) The nuclear symbol of the new isotope formed is \(\mathrm{^{272}Rg}\) (Rg-272), and (b) the nuclear symbol for the isotope after the third alpha particle emission is \(\mathrm{^{260}Db}\) (Db-260).

Step-by-step solution

Identify the given isotopes

We are given the isotopes Bi-209 and Ni-64. To understand them better, we need to know the number of protons (Z) and neutrons (N) in each. Bismuth (Bi) has an atomic number (Z) of 83, and Nickel (Ni) has an atomic number of 28. Number of protons and neutrons for the given isotopes: Bi-209: Z = 83, N = 209 - 83 = 126 Ni-64: Z = 28, N = 64 - 28 = 36

Calculate Z and N for isotope X

When Bi-209 is bombarded with Ni-64, one neutron is released, so we have one less neutron involved in the interaction. Therefore, the new isotope will have: Z = 83 + 28 = 111 N = 126 + 36 - 1 = 161

Find the element and write the nuclear symbol for isotope X (part a)

Element with atomic number 111 is Roentgenium (Rg). Thus, the nuclear symbol of the new isotope is: \(\mathrm{^{272}Rg}\) (Rg-272)

Calculate Z and N after three alpha particle emissions (part b)

An alpha particle consists of 2 protons and 2 neutrons. After three alpha emissions, our isotope will lose a total of 6 protons and 6 neutrons. New Z = 111 - 6 = 105 New N = 161 - 6 = 155

Find the element and write the nuclear symbol for isotope after three alpha particle emissions (part b)

An element with an atomic number of 105 is Dubnium (Db). Therefore, the nuclear symbol for the isotope after the third alpha particle emission is: \(\mathrm{^{260}Db}\) (Db-260)

Key concepts

Alpha Particle Emissions

Understanding alpha particle emissions is integral in the field of nuclear physics. Alpha particles are a type of ionizing radiation ejected from the nucleus of an atom. They consist of two protons and two neutrons bound together, identical to a helium nucleus. When an atom undergoes alpha decay, it emits an alpha particle, resulting in a new element with an atomic number decreased by two and a mass number decreased by four.

For instance, when the isotope undergoes three successive alpha emissions, as in our exercise, it's atomic and mass numbers will decrease with each emission. This is illustrated by subtracting six protons and six neutrons from the original isotope to find the new element formed.

Isotope Formation

An isotope is an atom with the same number of protons (atomic number) but a different number of neutrons (mass number) compared to other atoms of the same element. Isotopes can occur naturally, or they can be artificially produced through nuclear reactions, like bombarding a stable isotope with other particles.

In the exercise solution, the bombardment of Bi-209 with Ni-64 is an artificial creation of an isotope. This reaction creates Roentgenium-272, an isotope not found in nature, as it has more protons and neutrons than the most stable isotopes of Roentgenium. The nuclear symbol for this isotope is written as \( ^{272}Rg \), where 272 denotes the mass number, and Rg denotes the element Roentgenium.

Nuclear Reaction Equations

Nuclear reaction equations are used to represent the changes in the composition of the nucleus of an atom during nuclear reactions. These equations are balanced, meaning they follow the law of conservation of mass and charge. Both sides of the nuclear reaction will have the same total atomic number and the same total mass number even though individual particles and isotopes may change.

The nuclear reaction is represented by showing the starting isotopes, the particles involved in the reaction, and the new isotope or isotopes formed. In our exercise, the bombardment of Bi-209 with Ni-64, accompanied by the ejection of a neutron, leads to the formation of Roentgenium-272. After three alpha emissions, Roentgenium-272 becomes Dubnium-260. The careful accounting for protons and neutrons in each step ensures a balanced and informative nuclear equation.