Chapter 10, Problem 10.7E

Write appropriate symbols for the following particles using the ${}_Z^{A}X$ symbolism:

a. A tin- $117$ nucleus

b. A nucleus of the chromium $\left(\text{Cr}\right)$ isotope containing $26$ neutrons

c. A nucleus of element number $20$ that contains $24$ neutrons

Interpretation Introduction

(a)

Interpretation:

Then appropriate symbol for the given particles using the ${}_Z^{A}X$ symbolism is to be stated.

Concept introduction:

The atomic number of an element determines the number of protons and the number of electrons in a neutral atom. The mass number is the sum of a number of protons and the number of neutrons. An element is represented using the symbol ${}_Z^{A}X$ where A is the mass number and Z is the atomic number of the element X.

Answer to Problem 10.7E

The symbol of tin-$117$ nucleus is ${}_{\text{50}}^{\text{117}}\text{Sn}$.

Explanation of Solution

The given element is tin. The symbol of tin is $\text{Sn}$. The atomic number of tin is $50$. The given mass number of tin is $117$. An element can be represented using the symbol ${}_Z^{A}X$ where A is the mass number and Z is the atomic number of the element X. Therefore, the symbol of tin-$117$ nucleus is ${}_{\text{50}}^{\text{117}}\text{Sn}$.

Conclusion

The symbol of tin-$117$ nucleus is ${}_{\text{50}}^{\text{117}}\text{Sn}$.

Interpretation Introduction

(b)

Interpretation:

Then appropriate symbol for the given particles using the ${}_Z^{A}X$ symbolism is to be stated.

Concept introduction:

The atomic number of an element determines the number of protons and the number of electrons in a neutral atom. The mass number is the sum of a number of protons and the number of neutrons. An element is represented using the symbol ${}_Z^{A}X$ where A is the mass number and Z is the atomic number of the element X.

Answer to Problem 10.7E

The symbol of chromium $\left(\text{Cr}\right)$ isotope containing $26$ neutrons is ${}_{\text{24}}^{50}\text{Cr}$.

Explanation of Solution

The given element is chromium. The symbol of chromium is $\text{Cr}$. The atomic number of chromium is $24$ which is equal to the number of protons. The given number of neutrons in chromium is $26$. The mass number of an element can be calculated as follows.

$\text{Mass}\text{number}=\text{Number}\text{of}\text{protons}+\text{Number}\text{of}\text{neutrons}$

Substitute the values of a number of protons and that of neutrons in the above equation.

$\begin{array}{rll}\text{Mass}\text{number}& =& \text{Number}\text{of}\text{protons}+\text{Number}\text{of}\text{neutrons}\\ & =& \text{24}+\text{26}\\ & =& \text{50}\end{array}$

Therefore, the value of the mass number of chromium is $50$.

An element can be represented using the symbol ${}_Z^{A}X$ where A is the mass number and Z is the atomic number of the element X. Therefore, the symbol of chromium $\left(\text{Cr}\right)$ isotope containing $26$ neutrons is ${}_{\text{24}}^{50}\text{Cr}$.

Conclusion

The symbol of chromium $\left(\text{Cr}\right)$ isotope containing $26$ neutrons is ${}_{\text{24}}^{50}\text{Cr}$.

Interpretation Introduction

(c)

Interpretation:

Then appropriate symbol for the given particles using the ${}_Z^{A}X$ symbolism is to be stated.

Concept introduction:

The atomic number of an element determines the number of protons and the number of electrons in a neutral atom. The mass number is the sum of a number of protons and the number of neutrons. An element is represented using the symbol ${}_Z^{A}X$ where A is the mass number and Z is the atomic number of the element X.

Answer to Problem 10.7E

The symbol of the nucleus of the element number $20$ that contains $24$ neutrons is ${}_{\text{20}}^{44}\text{Ca}$.

Explanation of Solution

The atomic number of a given element is $20$, therefore, the given element is calcium. The symbol of calcium is $\text{Ca}$. The number of protons is equal to the atomic number. The given number of neutrons in calcium is $24$. The mass number of an element can be calculated as follows.

$\text{Mass}\text{number}=\text{Number}\text{of}\text{protons}+\text{Number}\text{of}\text{neutrons}$

Substitute the values of a number of protons and that of neutrons in the above equation.

$\begin{array}{rll}\text{Mass}\text{number}& =& \text{Number}\text{of}\text{protons}+\text{Number}\text{of}\text{neutrons}\\ & =& \text{20}+\text{24}\\ & =& \text{44}\end{array}$

Therefore, the value of the mass number of calcium is $44$.

An element can be represented using the symbol ${}_Z^{A}X$ where A is the mass number and Z is the atomic number of the element X. Therefore, the symbol of the nucleus of an element number $20$ that contains $24$ neutrons (calcium) is ${}_{\text{20}}^{44}\text{Ca}$.

Conclusion

The symbol of the nucleus of the element number $20$ that contains $24$ neutrons is ${}_{\text{20}}^{44}\text{Ca}$.