Q. 4.105 - An Introduction to General, Organic, and Biological Chemistry

Question

The most abundant isotope of lead is $\begin{array}{c}208\\ 82\end{array}Pb$.$(4.4,4.5)$

a. How many protons, neutrons, and electrons are in $\begin{array}{c}208\\ 82\end{array}Pb$?

b. What is the atomic symbol of another isotope of lead with $132$neutrons?

c.  What is the atomic symbol and name of an atom with the same mass number as in part b and $131$ neutrons?

Step-by-Step Solution

Answer

a. The number of electrons is $82$, neutrons is $126$ and protons is $82$.

b. The atomic symbol of another isotope of lead with $132$neutrons is $\begin{array}{c}214\\ 82\end{array}Pb$.

c. The atomic symbol and name of an atom with the same mass number as in part b and $131$ neutrons is $\begin{array}{c}214\\ 83\end{array}Bi$.

Part (a) step 1: Given Information

We need to find the number of protons, neutrons, and electrons in $\begin{array}{c}208\\ 82\end{array}Pb$.

Part (a) step 2: Simplify

The standard form is :  $\begin{array}{c}A\\ z\end{array}X$

Here, A is the mass number of atom

Z  atomic number of the element

 Mass Number $\left(A\right) =P + N$

$N=A-P =A-Z$

Here $Z=82 and A=208$

Therefore,

Number of electrons $\left(e^{-}\right)$- $82$

Number of protons $\left(p^{+}\right)$-  $82$

Number of neutrons $\left(N\right)$-  $208 -82 =126$

Part (b) step 1: Given Information

We need to find the atomic symbol of another isotope of lead with $132$neutrons.

Part (b) step 2: Simplify

Now,

The standard form is:  $\begin{array}{c}A\\ z\end{array}X$

Here, A is the mass number of atom

Z  atomic number of the element

Mass Number $\left(A\right) =P + N$

Here, 

Z= $82$ , N=$132$

A= $$\begin{gathered} 82+132 \\ =214 \end{gathered}$$

So, the symbol is $\begin{array}{c}214\\ 82\end{array}Pb$.

Part (c) step 1: Given Information

the atomic symbol and name of an atom with the same mass number as in part b and $132$ neutrons.

Part (c) step 2: Simplify

Mass number (A)=$214$

Neutrons (N)=$131$

The standard form for representation of an atom is- $\begin{array}{c}A\\ z\end{array}X$

Where A is the mass number of atom 

Z atomic number of the element 

Mass number $\left(A\right) = P+N$

$P = A - N = Z$

P =Z =$214-131=83$

The element in the periodic table at Z = $83$ is Bi(Bismuth) Therefore symbol is :

$\begin{array}{c}\begin{array}{c}214\\ 83\end{array}Bi\end{array}$