Formation of 17O Nucleus from 14N + Alpha Particle

[kihr]

Homework Statement

An alpha particle is bombarded on 14
N. As a result a 17
O nucleus is formed, and a particle is emitted. This particle is a: (a) neutron (b) proton (c) electron (d) positron. The answer is given as (b).

Homework Equations

The solution must take into account that the mass numbers have to balance on both sides of the equation.

The Attempt at a Solution

(c) and (d) get ruled out because they do not lead to a balance in mass numbers. Since the balance would be possible for both options (a) and (b) I need some clues as to why only (b) is acceptable.

 

[phyzguy]

What about the nuclear charge?

 

[kihr]

The mass number alone does not give an indication of the charge. The problem does not state the atomic numbers. Had this been given the question of my doubt would not have arisen. Looking forward to further inputs from you. Thanks.

 

[phyzguy]

The problem does not give the atomic numbers directly, but it tells you that the three nuclei are Nitrogen, Oxygen, and Helium (alpha particle). From this information you know the atomic numbers.

 

[paranormal]

As a scientist, my response to this content would be that the formation of a 17O nucleus from 14N and an alpha particle is a nuclear reaction that follows the law of conservation of mass and energy. In this reaction, an alpha particle (which is essentially a helium nucleus) is bombarded onto a nitrogen nucleus, resulting in the formation of a new oxygen nucleus and the emission of a particle. The emission of this particle is a result of the rearrangement of protons and neutrons in the nucleus to achieve a more stable configuration.

Now, to determine the nature of the emitted particle, we need to look at the mass numbers on both sides of the equation. On the reactant side, we have a mass number of 14 for nitrogen and a mass number of 4 for the alpha particle, giving us a total mass number of 18. On the product side, we have a mass number of 17 for oxygen and an unknown mass number for the emitted particle. In order for the law of conservation of mass to hold true, the total mass number on both sides must be equal.

Option (a) suggests that the emitted particle is a neutron, which has a mass number of 1. Adding this to the mass number of oxygen (17) would give us a total mass number of 18, which would balance the equation. However, this option does not consider the fact that the number of protons and neutrons in the nucleus must also be balanced. A neutron has 0 protons and 1 neutron, which would not match the number of protons and neutrons in an oxygen nucleus.

Option (b), on the other hand, suggests that the emitted particle is a proton, which has a mass number of 1. Adding this to the mass number of oxygen (17) would give us a total mass number of 18, which balances the equation. Additionally, a proton has 1 proton and 0 neutrons, which matches the number of protons and neutrons in an oxygen nucleus.

Therefore, based on the law of conservation of mass and the requirement for a balanced number of protons and neutrons in the nucleus, option (b) is the correct answer.