Chapter 19, Problem 12A

(a)

Interpretation Introduction

Interpretation: The nuclear reaction has to be completed by supplying the missing particle. The given reaction is,

  $\text{R}\text{a}\to ?+\text{R}\text{n}$

Concept Introduction : The decay of a nucleus by emitting an alpha particle $\left(\alpha \left(\text{or}\right)\text{H}\text{e}\right)$ is called as alpha emission. The general balanced equation is,

  $X\to \alpha +Y$

Answer to Problem 12A

The completed and balanced nuclear equation is,

  $\text{R}\text{a}\to \text{H}\text{e}+\text{R}\text{n}$

Explanation of Solution

The given reaction is,

  $\text{R}\text{a}\to ?+\text{R}\text{n}$

The decay of a nucleus by emitting an alpha particle $\left(\alpha \left(\text{or}\right)\text{H}\text{e}\right)$ is called as alpha emission. The general balanced equation is,

  $X\to \alpha +Y$

Where,

• $A$ is the mass number.
• $Z$ is the atomic number.
• $X$ is the original isotope.
• $Y$ is the new isotope.

Since the alpha particle consists of two protons, the newly formed nucleus has will have Z-2 protons. Change in number of protons change the nucleus. A new species is formed.

In radium $\left(\text{R}\text{a}\right)\text{,}$ the atomic number is $\text{88}$ and the mass number is $\text{226}\text{.}$

Mass number: The sum of the mass number should be equal on the both sides of the equation. Subtract the mass of the original nucleus with mass of new formed nucleus to get mass of the particle $\left(\text{226-222=4}\right)\text{.}$ The mass of the emitted particle is $\text{4}\text{.}$

Atomic number: The sum of the atomic number should be equal on the both sides of the equation. Subtract the atomic number of the original nucleus with atomic number of new formed nucleus to get atomic number of the emitted particle $\left(\text{86-84=2}\right)\text{.}$ The atomic number of the emitted particle is $\text{2}\text{.}$

From the periodic table, an element with atomic number 2 and mass number 4 is identified as helium, which is an alpha particle. Therefore, the missing particle in the nuclear equation is alpha particle $\left(\text{H}\text{e}\right)\text{.}$

The completed and balanced nuclear equation is,

  $\text{R}\text{a}\to \text{H}\text{e}+\text{R}\text{n}$

(b)

Interpretation Introduction

Interpretation: The nuclear reaction has to be completed by supplying the missing particle. The given reaction is,

  $\text{B}\text{e}+\text{H}\to ?+\text{H}\text{e}$

Concept Introduction : The decay of a nucleus by emitting an alpha particle $\left(\alpha \left(\text{or}\right)\text{H}\text{e}\right)$ is called as alpha emission. The general balanced equation is,

  $X\to \alpha +Y$

Answer to Problem 12A

The completed and balanced nuclear equation is,

  $Be+H\to Li+He$

Explanation of Solution

The given reaction is,

  $\text{B}\text{e}+\text{H}\to ?+\text{H}\text{e}$

The decay of a nucleus by emitting an alpha particle $\left(\alpha \left(\text{or}\right)\text{H}\text{e}\right)$ is called as alpha emission. The general balanced equation is,

  $X\to \alpha +Y$

Where,

• $A$ is the mass number.
• $Z$ is the atomic number.
• $X$ is the original isotope.
• $Y$ is the new isotope.

Since the alpha particle consists of two protons, the newly formed nucleus has will have Z-2 protons. Change in number of protons change the nucleus. A new species is formed.

The sum of the mass number should be equal on the both sides of the equation.

The sum of the atomic number should be equal on the both sides of the equation.

In the given reaction, the second nucleus on the right side of the equation should be mass number $\text{6}$ and atomic number $3$ to get a balanced nuclear equation.

From the periodic table, an element with atomic number $3$ is lithium. Therefore, the missing particle should be lithium.

The completed and balanced nuclear equation is,

  $Be+H\to Li+He$

(c)

Interpretation Introduction

Interpretation: The nuclear reaction has to be completed by supplying the missing particle. The given reaction is,

  $\text{O}+?\to \text{C}+\text{H}$

Concept Introduction : The process in which the electron from an inner orbital is absorbed into the nucleus of original isotope to form a new isotope is called as electron capture process.

The general equation is,

  $X+e\to Y$

Where,

• $A$ is the mass number.
• $Z$ is the atomic number.
• $X$ is the original isotope.
• $Y$ is the new isotope.

Answer to Problem 12A

The completed and balanced nuclear equation is,

  $\text{O}+e\to \text{C}+\text{H}$

Explanation of Solution

The given nuclear reaction is,

  $\mathrm{O}+?\to \text{C}+\text{H}$

In the above reaction, it can be seen that the mass number remains the same whereas the atomic number is decreased by one, therefore the missing particle should be an electron.

The completed and balanced nuclear equation is,

  $\text{O}+e\to \text{C}+\text{H}$