Chapter 2, Problem 36QAP

Myocardial perfusion imaging (MPI) is the latest tool used in the detection of coronary artery disease. It uses thallium-201 chloride. How many neutrons are in

(a) seventy atoms of thallium-201 ?

(b) one picogram $\left(1\times {10}^{-12}\text{g}\right)$ of thallium-201?

Interpretation Introduction

(a)

Interpretation:

To determine the number of neutrons in seventy atoms of thallium-201.

Concept introduction:

Chemical symbol (in short form) is written as:

$\begin{array}{l}\text{X- (mass}\text{number)}\\ \text{where,}\\ \text{X}\text{is}\text{symbol}\text{of}\text{element}\end{array}$

And relation between mass number, number of neutrons and number of protons in 1 atom of an element is given as:

$\text{Mass number = Number of protons in 1 atom+ Number of neutrons in 1 atom}$

For a neutral element:

Number of electrons in 1 atom = atomic number = number of protons in 1 atom

Answer to Problem 36QAP

In seventy atoms of thallium-201, there are 8400 neutrons.

Explanation of Solution

Here the chemical is symbol is given as thallium-201

i.e.Mass number of thallium-201 = 201

since atomic number of thallium is 81. Therefore,

Number of electrons in 1 atom= number of protons in 1 atom = 81

As we know:

Mass number = number of neutrons in 1 atom + number of protons in 1 atom

$\begin{array}{l}\begin{array}{l}\text{Therefore,}\hfill \\ \text{Number of neutrons in 1 atom = Mass number – number of protons in 1 atom}\hfill \\ \text{Number of neutrons in 1 atom = 201-81}\hfill \\ \text{Number of neutrons in 1 atom = 120}\hfill \end{array}\\ \therefore \text{Number of neutrons in 70 atoms = 120}\text{×70}\text{=}\text{8400}\text{neutrons}\end{array}$

Interpretation Introduction

(b)

Interpretation:

To determine the number of atoms in 1 picogram of thallium-201.

Concept introduction:

Relation between moles, mass of substance and number of atoms:

$\begin{array}{l}\text{moles}\text{=}\frac{\text{mass}\text{(g)}}{\text{molar}\text{mass}\text{(g/mol)}}\text{=}\frac{\text{number}\text{of}\text{atoms}}{{\text{N}}_{\text{A}}}\\ \text{where,}\\ {\text{N}}_{\text{A}}\text{represents}\text{avagadro’s}\text{number}\text{equal}\text{to}\text{6}{\text{.023×10}}^{\text{23}}\text{atoms/mol}\end{array}$

Chemical symbol (in short form) is written as:

$\begin{array}{l}\text{X- (mass}\text{number)}\\ \text{where,}\\ \text{X}\text{is}\text{symbol}\text{of}\text{element}\end{array}$

And relation between mass number, number of neutrons and number of protons in 1 atom of an element is given as:

$\text{Mass number = Number of protons in 1 atom+ Number of neutrons in 1 atom}$

For a neutral element:

Number of electrons in 1 atom = atomic number = number of protons in 1 atom

Answer to Problem 36QAP

Number of neutrons in 1 picogram of thallium-201 = $3.6\times {10}^{11}\text{neutrons}$.

Explanation of Solution

As we know:

$\text{moles}\text{=}\frac{\text{mass}\text{(g)}}{\text{molar}\text{mass}\text{(g/mol)}}\text{=}\frac{\text{number}\text{of}\text{atoms}}{{\text{N}}_{\text{A}}}$

Therefore,

$\frac{\text{mass}\text{(g)}}{\text{molar}\text{mass}\text{(g/mol)}}\text{=}\frac{\text{number}\text{of}\text{atoms}}{{\text{N}}_{\text{A}}}$

According to question:

Mass of thallium-201= 1 picogram = 1×10-12 g (because 1 picogram = 10-12 gram)

Molar mass of thallium-201= 200.978 g/mol

Plugging values in above formula, we get:

$\begin{array}{l}\frac{\text{mass}\text{(g)}}{\text{molar}\text{mass}\text{(g/mol)}}\text{=}\frac{\text{number}\text{of}\text{atoms}}{{\text{N}}_{\text{A}}\text{(atoms/mol)}}\\ \frac{\text{1}\times {\text{10}}^{\text{-12}}}{200.971}\text{=}\frac{\text{number}\text{of}\text{atoms}}{\text{6}{\text{.023×10}}^{\text{23}}}\\ \Rightarrow \text{number}\text{of}\text{atoms}\text{=}\frac{\text{6}{\text{.023×10}}^{\text{23}}\text{×1}\times {\text{10}}^{\text{-12}}}{200.971}\\ \Rightarrow \text{number}\text{of}\text{atoms}\text{=}3.0\times {10}^9\text{atoms}\end{array}$

Hence, 3.0 ×10⁹atoms are present in 1 picogram of thallium-201.

Here the chemical is symbol is given as thallium-201

i.e.Mass number of thallium-201 = 201

since atomic number of thallium is 81. Therefore,

Number of electrons in 1 atom= number of protons in 1 atom = 81

As we know:

Mass number = number of neutrons in 1 atom + number of protons in 1 atom

$\begin{array}{l}\begin{array}{l}\text{Therefore,}\hfill \\ \text{Number of neutrons in 1 atom = Mass number – number of protons in 1 atom}\hfill \\ \text{Number of neutrons in 1 atom = 201-81}\hfill \\ \text{Number of neutrons in 1 atom = 120}\hfill \end{array}\\ \therefore \text{Number of neutrons in 3}\text{.0}\times {\text{10}}^{\text{9}}\text{ atoms = 120}\text{×3}\text{.0}\times {\text{10}}^{\text{9}}\text{=}3.6\times {10}^{11}\text{neutrons}\end{array}$