Q. 5.58 - An Introduction to General, Organic, and Biological Chemistry

Question

Determine the number of protons and number of neutrons in the nucleus of each of the following: $(5.1)$

a. boron-$10$

b. zinc- $72$

c. iron- $59$

d. gold- $198$

Step-by-Step Solution

Answer

The nucleus is calculated as  

(part a) There are $5$protons and $5$ neutrons

(part b) There are $30$ protons and $42$ neutrons

(part c) There are $26$ protons and $33$ neutrons

(part d) There are $79$ protons and $119$ neutrons

Step 1- Given Information (part a)

(part a) The mass number is the sum of the number of protons and the number of neutrons. 

$Mass number = Number of protons + Number of neutrons$

The number of neutrons is calculated using the above formula. $Number of neutrons = Mass number - Number of protons$

The atomic number indicates the number of protons. 

Step 2- Explanation (part a)

(part b) For boron, $-10, 10$ is the mass number of boron and the atomic number of boron is $5.$ Therefore, the number of protons is also$5$. Therefore, the number of neutrons is calculated by substituting the mass number and the number of protons in the above equation.

$Number of neutrons = Mass number - Number of protons$

$Number of neulrons =10-5$

                                         $=5$

Therefore, Bor $-10$ has $5$ protons and $5$ neutrons.

Step -3- Explanation (part b)

(part a) For zinc, $- 72.72$ is the mass number of zinc 

$The atomic number of zinc is 30 .$

$Number of protons =30$

Therefore, the number of neutrons is calculated by substituting the mass number and the number of protons in the above equation.

$Number of neutrons = Mass number - Number of protons$

$Number of neutrons =72-30$

                                        $=42$

Therefore, zinc $-72$ has  $30$protons and $42$neutrons. 

Step 4 - Explanation (part c)

(part b) For iron$-59, 59$ is the mass number of iron. The atomic number of iron is $26$. Therefore, the number of protons is $26$. The number of neutrons is calculated by substituting the mass number and the number of protons in the above equation. 

$Number of neutrons = Mass number - Number of protons$

$Number of neutrons =59-26$

                                             $=33$

Therefore, iron $- 59$ has $26$ protons and $33$ neutrons.

Step 5 - explanation (part d)

(part c) In gold $-198, 198$ is the mass number of gold. The atomic number of gold is $79$. Therefore, the number of protons is $79$. Therefore, the number of neutrons is calculated by substituting the mass number and the number of protons in the above equation.

$Number of neutrons= Mass number- Number of protons$

$Number of neutrons =198-79$

                                         $=119$

Therefore, gold $-198$ has $79$ protons and $119$ neutrons.