Question

When bismuth-209 is bombarded with nickel-64, one neutron and a new isotope, \(\mathrm{X}\), is 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: The nuclear symbol for the new isotope formed after the initial reaction is ^{272}_{111}X. After three alpha particle emissions, the nuclear symbol for the resulting isotope is ^{260}_{105}X.

Step-by-step solution

(a) Identifying the new isotope formed in the initial reaction)

When Bismuth (Bi-209) is bombarded with Nickel (Ni-64), one neutron is formed along with a new isotope, X. Using the conservation of nucleons, we set up the following equation: Bi-209 + Ni-64 = n + X Now we know that Bismuth has 83 protons and Nickel has 28 protons. Also, a neutron has no charge (0 protons). So the isotope, X, must have: (83+28) protons = 111 protons Since conservation of nucleons must hold: (209 + 64) = (1 + A_X) Where A_X represents the mass number of isotope X. Solving for A_X gives: A_X = (209 + 64) - 1 = 272 The new isotope has 111 protons and a mass number of 272. Therefore, the nuclear symbol for this isotope is: \(^{272}_{111}\)X

(b) Identifying the isotope formed after third alpha particle emission)

Each alpha particle contains 2 protons and has a mass number of 4. After three successive alpha emissions, the isotope will lose a total of 2*3 = 6 protons and 4*3 = 12 mass units. So the resulting isotope after the third alpha emission will have: Protons: 111 - 6 = 105 Mass Number: 272 - 12 = 260 The symbol for the isotope after the third alpha particle emission is: \(^{260}_{105}\)X

Key concepts

Bismuth Bombardment

In the fascinating field of nuclear chemistry, 'bismuth bombardment' refers to a process involving the collision of a bismuth atom with another particle, typically to synthesize new elements or isotopes. Take bismuth-209, for example, which is a stable isotope. When it encounters a high-speed particle like nickel-64, the result is a complex nuclear reaction.

Bismuth-209 contains 83 protons in its nucleus, while nickel-64 contains 28. During the bombardment, these two nuclei merge, momentarily creating a very heavy, unstable nucleus that quickly sheds a neutron and rearranges itself into a new isotope, named 'X' in our exercise. To understand which isotope 'X' is, we apply the law of conservation of mass and atomic number. These laws state that the total number of nucleons (protons plus neutrons) and the total number of protons must be the same before and after the reaction.

To calculate 'X', we sum the atomic numbers (83 for bismuth + 28 for nickel) to get the atomic number for 'X', which is 111, representing an element not found naturally on Earth. The same applies to the mass numbers; by adding bismuth's and nickel's mass numbers and subtracting one neutron, we get the mass number for 'X'. This type of reaction is not only crucial for producing new elements but also for understanding the forces and interactions that govern atomic nuclei.

Nickel-Induced Nuclear Reaction

Unlocking New Elements

Nickel-induced nuclear reactions are a powerful means to create new, heavier elements that do not exist naturally on our planet. In our exercise, the relationship between nickel-64 and bismuth-209 is a perfect example of how these reactions work in the field of synthetic element creation.

When nickel, which serves as a projectile, crashes into a bismuth target, the intense energy and forces involved can overcome the repulsion between two positively charged nuclei. This is the critical event that enables the two different elements to fuse and form a new isotope. These reactions are performed in particle accelerators, where conditions are precisely controlled to facilitate the fusion.

Particle accelerators play an indispensable role in this field, allowing scientists to break through the limitations of the periodic table as we know it. It’s important for students to recognize that nickel is not just a fundamental part of a coin but also a key player in groundbreaking nuclear chemistry.

Alpha Particle Emissions

Alpha particle emissions are types of radioactive decay and a cornerstone in nuclear chemistry. An alpha particle is essentially a helium nucleus consisting of two protons and two neutrons. In our exercise, after the formation of isotope 'X', the unstable nucleus undergoes a series of alpha particle emissions in an attempt to reach a more stable state.

Each emission results in the isotope losing two protons and two neutrons, equivalent to a mass number decrease of four. This not only changes the mass of the isotope but also its atomic number, thus transforming it into a different element altogether. After three such emissions, as noted in the exercise, we see a significant transformation in the isotope 'X', shifting it 6 places back in the periodic table (because it has lost 6 protons) and shedding 12 units of mass.

Alpha emissions can be highly enlightening for students as they highlight the natural processes through which elements can undergo transmutation, reminiscent of the alchemists' dream to turn lead into gold, albeit on a subatomic scale. Understanding this decay process also sheds light on the mechanisms governing the stability of elements and isotopes, and it plays a crucial role in fields ranging from nuclear power generation to medical diagnostics and treatments.