When boron nucleus (10_5 B) is bombarded by neutrons, alpha-particles are emitted. The resulting nuc

Q: What exactly is an alpha particle?

An alpha particle is a Helium nucleus, consisting of 2 protons and 2 neutrons. It is represented as $^{4}_{2}\text{He}$.

Q: Why do we balance $Z$ and $A$ in a nuclear reaction?

Balancing $Z$ ensures the conservation of electric charge, while balancing $A$ ensures the conservation of the total number of nucleons (baryon number).

Q: How do I know which element corresponds to $Z=3$?

You need to remember the first few elements of the periodic table: Hydrogen ($Z=1$), Helium ($Z=2$), Lithium ($Z=3$), Beryllium ($Z=4$), Boron ($Z=5$), etc.

Q: Does the neutron have an atomic number?

No, a neutron has no protons, so its atomic number $Z$ is 0. Its mass number $A$ is 1.

Q: Is energy conserved in this reaction?

Yes, the total mass-energy is conserved. The difference in rest mass between reactants and products is converted into the kinetic energy of the products, known as the Q-value.

Question

When boron nucleus $\left(^{10}_{5}	ext{B}ight)$ is bombarded by neutrons, $\alpha$-particles are emitted. The resulting nucleus is of the element ........... and has the mass number…… .

Sigma Percentile · Accepted Answer

### Analyzing the Setup

Imagine you are in a nuclear physics laboratory. We are given a target nucleus of Boron-10, denoted as $^{10}_{5}	ext{B}$. This nucleus is being bombarded by neutrons. A neutron is a subatomic particle with no charge and a mass number of 1, represented as $^{1}_{0}	ext{n}$.

When the neutron strikes the Boron-10 nucleus, a nuclear reaction occurs, and an $\alpha$-particle is emitted. An $\alpha$-particle is essentially a Helium nucleus, which consists of 2 protons and 2 neutrons. Thus, it is represented as $^{4}_{2}	ext{He}$. Our goal is to identify the unknown resulting nucleus.

### The Master Equation

In any nuclear reaction, two fundamental conservation laws must be obeyed:
1. **Conservation of Atomic Number ($Z$):** The total number of protons before the reaction must equal the total number of protons after the reaction.
2. **Conservation of Mass Number ($A$):** The total number of nucleons (protons + neutrons) before the reaction must equal the total number of nucleons after the reaction.

Let the unknown resulting nucleus be denoted as $^{A}_{Z}	ext{X}$. We can write the complete nuclear equation as:
$$ ^{10}_{5}	ext{B} + ^{1}_{0}	ext{n} \longrightarrow ^{4}_{2}	ext{He} + ^{A}_{Z}	ext{X} $$

### Final Calculation

Let's apply the conservation laws to find $Z$ and $A$.

**Balancing the Atomic Number ($Z$):**
Looking at the subscripts (atomic numbers) on both sides of the equation:
$$ 5 + 0 = 2 + Z $$
$$ Z = 3 $$
The atomic number $Z = 3$ corresponds to the element **Lithium (Li)**.

**Balancing the Mass Number ($A$):**
Now, looking at the superscripts (mass numbers) on both sides:
$$ 10 + 1 = 4 + A $$
$$ 11 = 4 + A $$
$$ A = 7 $$

The resulting nucleus has an atomic number of 3 and a mass number of 7. Therefore, the unknown nucleus is **Lithium-7**, written as $^{7}_{3}	ext{Li}$.

The element is **Lithium** and its mass number is **7**.

Animated Solution for Physics - Atoms and Nuclei: When boron nucleus $(_{5}^{10} B)$ is bombarded by neutrons, $α$ -particles are emitted. The resulting nucleus is of the element ........... and has the mass number…… .

Visualized Solution

\text{Reactants}

\text{Conservation Laws}

\text{Nuclear Equation}

\text{Finding } Z

\text{Finding } A

\text{Product Nucleus}

\text{Q-value}

The Sigma Insight: Nucleus and Nuclear Reaction

Analyzing the Setup

The Master Equation

Final Calculation

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