Chapter 4, Problem 126A

Interpretation Introduction

Interpretation:

The number of protons and neutrons for each of the Zirconium isotopes needs to be determined.

Concept introduction:

An element consists of three subatomic particles: electrons, protons, and neutrons. The atomic nucleus is made up of neutrons and protons. In any element, the number of protons and electrons is always same but the number of neutrons will be different. Mass of number is calculated by:

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

Answer to Problem 126A

The numbers of protons are same in each isotope that is 40 but the number of neutrons are different that is ${\text{Zr}}^{90}$ $=50$, ${\text{Zr}}^{91}$$=51$, ${\text{Zr}}^{92}$ $=52$, ${\text{Zr}}^{94}$ $=54$, ${\text{Zr}}^{96}$ $=56$ respectively.

Explanation of Solution

Given information:

The given table

The Relative abundance of zirconium isotopes
Element	Mass (amu)	Abundance (%)
Zirconium-90	$89.905$	$51.45$
Zirconium-91	$90.906$	$11.22$
Zirconium-92	$91.905$	$17.15$
Zirconium-94	$93.906$	$17.38$
Zirconium-96	$95.908$	$2.8$

The atomic mass is equal to the mass number of the isotope.

The number of protons is $40$for all isotope of zirconium.

$\text{Atmoic}\text{mass=}\text{number}\text{of}\text{protons + number}\text{of}\text{neutrons}$

For the ${\text{Zr}}^{90}$

$\text{number}\text{of}\text{neutron=mass}\text{number-number}\text{of}\text{protons}$

$=90-40$

$=50.$

For the ${\text{Zr}}^{91}$

$\text{number}\text{of}\text{neutron=mass}\text{number-number}\text{of}\text{protons}$

$=91-40$

$=51.$

For the ${\text{Zr}}^{92}$

$\text{number}\text{of}\text{neutron=mass}\text{number-number}\text{of}\text{protons}$

$=92-40$

$=52.$

For the ${\text{Zr}}^{94}$

$\text{number}\text{of}\text{neutron=mass}\text{number-number}\text{of}\text{protons}$

$=94-40$

$=54.$

For the ${\text{Zr}}^{96}$

$\text{number}\text{of}\text{neutron=mass}\text{number-number}\text{of}\text{protons}$

$=96-40$

$=56.$

Conclusion

Neutrons $=50,51,52,54,56$ and protons $=40$ for all.