Chapter 2, Problem 2.45P

Interpretation Introduction

Interpretation:

The given table is to be completed for the given neutral elements.

Concept introduction:

The electrons in the atoms revolve around the nucleus in different orbits. The nucleus of the atom has two particles, protons and neutrons. The number of proton is the atomic number and the sum of the proton and neutron is the mass number of the atom.

Answer to Problem 2.45P

The complete table is as shown below.

	Element Symbol	Atomic number	Mass Number	Number of Protons	Number of Neutrons	Number of Electrons
a	$\text{C}$	$6$	$12$	$6$	$6$	$6$
b	$\text{P}$	$15$	$31$	$15$	$16$	$15$
c	$\text{Zn}$	$30$	$65$	$30$	$35$	$30$
d	$\text{Mg}$	$12$	$24$	$12$	$12$	$12$
e	$\text{I}$	$53$	$127$	$53$	$74$	$53$
f	$\text{Be}$	$4$	$9$	$4$	$5$	$4$
g	$\text{Zr}$	$40$	$91$	$40$	$51$	$40$
h	$\text{S}$	$16$	$32$	$16$	$16$	$16$

Explanation of Solution

All the elements are assigned a letter symbol from their name. The symbol is the first or first two letters from the name of the element.

The atomic number of an element is the number of protons in its atom.

The mass number of the element is the sum of the numbers of protons and neutrons present in the nucleus of the atom.

The protons and neutrons are present in the nucleus of the atom and electrons revolve around the nucleus. The number of electrons and protons are equal in a neutral atom as the electrons and protons are charged bodies.

To complete the given table, the points given above are to be considered.

For the case (a), the data given is the symbol of element $\text{C}$ and its mass number $12$.

So,

The symbol $\text{C}$ is given to the element, carbon with atomic number $6$ . The the atomic number is equal to the number of protons and electrons in the atom. Therefore, carbon has $6$ electrons as well as $6$ protons. Its mass number is $12$.

The number of neutrons is calculated by the formula given below.

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

Substitute the given values in the above formula.

  $\begin{array}{c}\text{Mass}\text{number}=\text{Number}\text{of}\text{neutrons}+\text{Number}\text{of}\text{protons}\\ 12=\text{Number}\text{of}\text{neutrons}+6\\ \text{Number}\text{of}\text{neutrons}=12-6\\ =6\end{array}$

Hence, carbon with element symbol $\text{C}$ has $6$ electrons, $6$ protons and $6$ neutrons. Its atomic number is $6$ and mass number is $12$.

For the case (b) the data given is its mass number $31$ and number of electron is $15$.

So, the atomic number is equal to the number of protons and electrons in the atom. This atom has $15$ electrons and $15$ protons as well. Its atomic number is $15$ . Its mass number is $31$.

The number of neutrons can be calculated by the formula given below.

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

Substitute the given values in the formula below.

  $\begin{array}{c}\text{Mass}\text{number}=\text{Number}\text{of}\text{neutrons}+\text{Number}\text{of}\text{protons}\\ 31=\text{Number}\text{of}\text{neutrons}+15\\ \text{Number}\text{of}\text{neutrons}=31-15\\ =16\end{array}$

So, the element is phosphorus as its atomic number is $15$ with symbol $\text{P}$ . It has $15$ electrons, $15$ protons and $16$ neutrons. Its atomic number is $15$ and mass number is $31$.

For the case (c), the data given is its number of neutrons $35$ , and number of electrons $30$.

So, the atomic number is equal to the number of protons and electrons in the atom. This atom has $30$ electrons therefore $30$ protons as well. Its atomic number is $30$.

Its number of neutrons is $35$ . The mass number can be calculated by the formula given below.

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

Substitute the given values in the above formula

  $\begin{array}{c}\text{Mass}\text{number}=\text{Number}\text{of}\text{neutrons}+\text{Number}\text{of}\text{protons}\\ =35+30\\ =16\end{array}$

So, the element is zinc as its atomic number is $30$ with symbol $\text{Zn}$ . It has $30$ electrons and $30$ protons and $35$ neutrons. Its atomic number is $30$ and mass number is $65$.

For the case (d), the data given is the symbol of element $\text{Mg}$ and its mass number $24$.

So, the symbol $\text{Mg}$ is given to the magnesium with atomic number $12$ . As the atomic number is equal to the number of protons and electrons in the atom, therefore magnesium has $12$ electrons as well as $12$ protons. Its mass number is $24$.

The number of neutrons can be calculated by the formula given below.

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

Substitute the given values in the above formula.

  $\begin{array}{c}\text{Mass}\text{number}=\text{Number}\text{of}\text{neutrons}+\text{Number}\text{of}\text{protons}\\ 24=\text{Number}\text{of}\text{neutrons}+12\\ \text{Number}\text{of}\text{neutrons}=24-12\\ =12\end{array}$

So, the magnesium element with symbol $\text{Mg}$ has $12$ electrons and $12$ protons and $12$ neutrons. Its atomic number is $12$ and mass number is $24$.

For the case (e), the data given is its number of neutrons $74$ , and number of protons $53$.

So, the atomic number is equal to the number of protons and electrons in the atom. This atom has $53$ electrons therefore $53$ protons as well.

Its atomic number is $53$ . Its number of neutrons is $74$ . The mass number can be calculated by the formula given below.

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

Substitute the given values in the above formula

  $\begin{array}{c}\text{Mass}\text{number}=\text{Number}\text{of}\text{neutrons}+\text{Number}\text{of}\text{protons}\\ =74+53\\ =127\end{array}$

So the element is iodine as its atomic number is $53$ with symbol $\text{I}$ . It has $53$ electrons and $53$ protons and $74$ neutrons. Its atomic number is $53$ and mass number is $127$.

For the case (f), the data given is its atomic number $4$ and number of neutron is $5$.

So, the atomic number is equal to the number of protons and electrons in the atom. Its atomic number is $4$ . Therefore this atom has $4$ electrons and $4$ protons as well. Its number of neutron is $5$.

The mass number of the element can be calculated by the formula given below.

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

Substitute the given values in the formula below.

  $\begin{array}{c}\text{Mass}\text{number}=\text{Number}\text{of}\text{neutrons}+\text{Number}\text{of}\text{protons}\\ =\text{4}+5\\ =9\end{array}$

So the element is beryllium as its atomic number is $4$ with symbol $\text{Be}$ . It has $4$ electrons, $4$

protons and neutrons. Its atomic number is $4$

and mass number is

For the case (g) the data given is its atomic number $40$ and mass number is $91$.

So, the atomic number is equal to the number of protons and electrons in the atom. Its atomic number is $40$ . Therefore this atom has $40$ electrons and $40$ protons as well. Its mass number is $91$.

The number of neutron of the element can be calculated by the formula given below.

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

Substitute the given values in the above formula

  $\begin{array}{c}\text{Mass}\text{number}=\text{Number}\text{of}\text{neutrons}+\text{Number}\text{of}\text{protons}\\ 91=\text{Number}\text{of}\text{neutrons}+\text{40}\\ \text{Number}\text{of}\text{neutrons}=91-40\\ =51\end{array}$

So the element is zirconium as its atomic number is $40$ with symbol $\text{Zr}$ . It has $40$ electrons, $40$ protons and $51$ neutrons. Its atomic number is $40$ and mass number is $91$.

For the case (h), the number of neutrons is $16$ , and number of electrons is $16$.

So, the atomic number is equal to the number of protons and electrons in the atom. This atom has $16$ electrons therefore $16$ protons as well. Its atomic number is $16$ . Its number of neutrons is $16$.

The mass number can be calculated by the formula given below.

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

Substitute the given values in the formula below.

  $\begin{array}{c}\text{Mass}\text{number}=\text{Number}\text{of}\text{neutrons}+\text{Number}\text{of}\text{protons}\\ =16+16\\ =32\end{array}$

So the element is sulfur as its atomic number is $16$ with symbol $\text{S}$ . It has $16$ electrons and $16$ protons and $16$ neutrons. Its atomic number is $16$ and mass number is $32$.

Conclusion

The table is completed with the symbols of elements and the information about their atoms and nucleus.