Question

When \({ }_{13} \mathrm{Al}^{27}\) is bombarded with \(\alpha\) particle, a radioactive isotope of phosphorus \({ }_{1 s} \mathrm{P}^{30}\) is formed. Which particle is emitted along with \({ }_{15} \mathrm{P}^{30}\) ? (a) deuteron (b) proton (c) electron (d) neutron

Short answer

The emitted particle is a neutron (d).

Step-by-step solution

Understand the Nuclear Reaction

In this reaction, aluminum is bombarded by an alpha particle, resulting in the formation of a phosphorus isotope. The nuclear reaction equation can be written as \( {}_{13}^{27}\text{Al} + {}_{2}^{4}\text{He} \rightarrow {}_{15}^{30}\text{P} + X \), where \( X \) is the particle we need to identify.

Calculate the Mass Number Conservation

The conservation of mass number requires that the sum of mass numbers on the left side of the reaction equals the sum on the right side. Initially, the mass numbers are 27 (Al) + 4(He) = 31. After the reaction, it's 30 for phosphorus, so \( A_x + 30 = 31 \). This means the mass number of \( X \) is 1.

Calculate the Atomic Number Conservation

The conservation of atomic number requires that the sum of atomic numbers on the left equals the sum on the right. Initially, the atomic numbers are 13 (Al) + 2(He) = 15. After the reaction, it's 15 for phosphorus, so \( Z_x + 15 = 15 \). This means the atomic number of \( X \) is 0.

Identify the Emitted Particle

With mass number 1 and atomic number 0, the emitted particle corresponds to a neutron (\( {}_{0}^{1}\text{n} \)). Therefore, the particle emitted along with \( {}_{15}^{30}\text{P} \) is a neutron.

Key concepts

Alpha Particle

An alpha particle is a type of nuclear particle that plays a crucial role in nuclear reactions. It consists of two protons and two neutrons. Essentially, an alpha particle is the same as a helium nucleus.

Alpha particles are positively charged and have relatively high mass compared to other nuclear particles such as beta particles or neutrons. In nuclear reactions, when an alpha particle is emitted, it often forms a new element or isotope, usually with a decreased atomic number.

• Alpha particle = 2 protons + 2 neutrons
• Same as a helium nucleus
• Positively charged and relatively heavy

This particle is responsible for rearrangements at the nuclear level, resulting in changes to both atomic and mass numbers, as illustrated in our original exercise.

Phosphorus Isotope

In nuclear chemistry, isotopes refer to atoms of the same element with the same atomic number but different mass numbers. The case of phosphorus in the original exercise demonstrates this concept effectively.

A phosphorus isotope is a form of the chemical element phosphorus that contains the usual 15 protons but has a mass number of 30, instead of the more common mass numbers like 31 found in nature. This particular isotope, { }_{15} ext{P}^{30}, is produced as a result of the nuclear reaction involving an alpha particle.

• Isotopes have the same atomic number but different mass numbers
• Phosphorus isotope in the exercise has 15 protons and a mass number of 30
• Can be radioactive due to the unstable nucleus formed during the reaction

The formation of such isotopes is intrinsic to understanding how nuclear reactions can create new forms of elements.

Mass Number Conservation

The principle of mass number conservation is fundamental in nuclear reactions.

This principle states that the sum of the mass numbers of the reactants must equal the sum of the mass numbers of the products. In our exercise, the mass numbers on the left side, consisting of { }_{13}^{27} ext{Al} and { }_{2}^{4} ext{He} total to 31. After the reaction, { }_{15}^{30} ext{P} is formed, accounting for 30 mass units.

The simplification comes with the realization that the missing 1 mass unit corresponds to another particle, which in this exercise, is identified as a neutron.

• Total mass on reactants' side = Total mass on products' side
• Ensures no mass is lost, just transformed
• Essential for identifying missing particles during reactions

This conservation helps predict resultant products in unknown nuclear reactions by ensuring that mass is conserved.

Atomic Number Conservation

Alongside mass number conservation, atomic number conservation is pivotal in understanding nuclear reactions.

This concept suggests that the sum of atomic numbers of the reactants equals the sum of atomic numbers of the products. In our problem, the left side of the equation has aluminum and an alpha particle contributing a total atomic number of 15. For the resultant phosphorus isotope of atomic number 15, another particle must have an atomic number of 0.

• Total atomic number on reactants' side = Total atomic number on products' side
• Ensures elements transform without losing protons
• Helps in identifying the types of particles involved

In this scenario, the missing particle is found to be a neutron, which fits as it has no charge and therefore does not alter the atomic number when added to phosphorus.