Question

In the nuclear transmutation \({ }_{4}^{9} \mathrm{Be}+\mathbf{X} \longrightarrow{ }_{4}^{8} \mathrm{Be}+\mathbf{Y}\) \((\mathbf{X}, \mathbf{Y})\) is \((\) are \()\) (A) \((\gamma, n)\) (B) \((p, D)\) (C) \((n, D)\) (D) \((\gamma, p)\)

Short answer

(C) (n, D)

Step-by-step solution

Identify the Conservation Laws

Nuclear reactions must obey the conservation laws, including the conservation of mass number (A) and the conservation of atomic number (Z). The mass number is the sum of protons and neutrons, and the atomic number is the number of protons in the nucleus.

Analyze the Given Reaction

In the given reaction, \({ }_{4}^{9} \text{Be} + \text{X} \rightarrow { }_{4}^{8} \text{Be} + \text{Y}\), we use the conservation laws to identify the particles X and Y. The mass number and atomic number on both sides of the reaction should be equal.

Calculate Changes in Mass and Atomic Numbers

The mass number on the left is 9 (from Be) plus the mass number of X. On the right side, it is 8 (from Be) plus the mass number of Y. For atomic numbers, we have 4 from beryllium on both sides. Let's denote the mass number of X as A and its atomic number as Z, then for Y, it is A-1 and Z respectively.

Solve for X and Y

Since the atomic number (Z) for Be does not change, the particle X cannot change the number of protons, suggesting that X may be a neutron (n) or a gamma photon (\(\gamma\)), which has neither mass nor charge. However, for the mass number to decrease by 1, as from 9 to 8, the particle X must be converted to Y by emitting a neutron. Thus X cannot be a gamma photon. Thereby, X is a neutron (n), and Y is a particle with one less mass number than X but the same atomic number, which by definition is deuterium (D), a nucleus consisting of one proton and one neutron.

Key concepts

Conservation Laws in Physics

Physics operates on a fundamental principle that certain quantities are conserved through transformations. These are famously known as conservation laws. In nuclear transmutation, two significant conservation laws are paramount: the conservation of mass number and the conservation of atomic number.

• The mass number (A) indicates the total number of protons and neutrons in an atomic nucleus. During nuclear reactions, the mass number must remain constant before and after the transformation.
• The atomic number (Z) reflects the number of protons found in the nucleus. This number is crucial as it defines the chemical element of the atom, and hence must be conserved in any reaction.

These laws ensure that while particles may change type or be emitted, the overall balance of mass and atomic identity is maintained. When solving problems involving nuclear transmutation, checking these conservation laws often leads directly to the identification of the particles involved in the reaction.

Mass Number

The mass number plays a crucial role in nuclear chemistry and physics. Represented by the symbol A, it is equal to the sum of the number of protons and neutrons within an atomic nucleus.

• Mass number is not the same as atomic mass, which is measured in atomic mass units; mass number is a whole number.
• Isotopes of a chemical element have the same atomic number (number of protons) but different mass numbers because they contain different numbers of neutrons.
• In nuclear reactions, if a neutron is converted into a proton, the mass number remains unchanged since both particles contribute to it.
• However, if a neutron is emitted or absorbed, the mass number of the nucleus will decrease or increase by one, respectively.

Understanding the mass number is essential in analyzing nuclear reactions, as seen in the exercise, where the loss of a neutron resulted in a decrease in the mass number from 9 to 8.

Atomic Number

The atomic number, denoted by Z, is another fundamental concept in nuclear physics. It is defined as the number of protons in the nucleus of an atom and it determines the chemical identity of the element.

• Every element on the periodic table is unique and is characterized by its atomic number.
• Changing the number of neutrons does not affect the atomic number, which is why isotopes of an element have the same atomic number but different mass numbers.
• When a nuclear reaction occurs, such as the emission or absorption of a particle, the atomic number will change if and only if that particle is a proton or contains protons.

In our exercise, the fact that the atomic number remains constant at 4 before and after the nuclear transmutation suggests that the identity of the element (beryllium, in this case) does not change. This piece of information is key to deducing that in the reaction given, the particle absorbed or emitted cannot be a proton or contain protons because the atomic number does not change.