Chapter 4, Problem 127A

Interpretation Introduction

Interpretation:

The number of neutrons or protons is same in atom needs to be explained.

Concept introduction:

An element consists of three subatomic particles: electrons, protons, and neutrons. The atomic nucleus is made up of neutrons and protons. Mass of number is calculated by:

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

Answer to Problem 127A

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

Explanation of Solution

The given table is:

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.

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

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

The number of protons = $40$.

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

$=90-40$

$=50.$

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

The number of protons = $40$.

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

$=91-40$

$=51.$

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

The number of protons = $40$.

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

$=92-40$

$=52.$

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

The number of protons = $40$.

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

$=94-40$

$=54.$

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

The number of protons = $40$.

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

$=96-40$

$=56.$

From the calculation, it is proved that the number of protons is the same, whereas, the number of neutrons is changed. The main reason behind this is the number of protons is what determines the element. So, if it is changed, this means that the element is changed to another element, while neutrons can increase as the element becomes radioactive element.

Conclusion

In any element, the number of protons and electrons is always same but the number of neutrons will be different.