# In a Periodic Table the Average Atomic Mass of Magnesium is Given as 24.312 U. the Average Value is Based on Their Relative Natural Abundance on Earth Calculate the Abundances of Other Two Isotopes. - Physics

In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are ""_12^24Mg (23.98504u),  ""_12^25 Mg (24.98584u) and ""_12^26Mg (25.98259u). The natural abundance of ""_12^24 Mg is 78.99% by mass. Calculate the abundances of other two isotopes.

#### Solution

Average atomic mass of magnesium, m = 24.312 u

Mass of magnesium isotope ""_12^24  Mg, m1 = 23.98504 u

Mass of magnesium isotope""_12^25  Mg, m= 24.98584 u

Mass of magnesium isotope ""_12^26  Mg, m= 25.98259 u

Abundance of ""_12^24  Mg, η1= 78.99%

Abundance of ""_12^25  Mg, ηx%

Hence, abundance of ""_12^26  Mg, η= 100 − x − 78.99% = (21.01 − x)%

We have the relation for the average atomic mass as:

m = (m_1eta_1 + m_2eta_2 + m_3eta_3)/(eta_1 + eta_2 + eta_3)

24.312 = (23.98504 xx 78.99 + 24.98584  xx x + 25.98259 xx (21.01 - x))/100

2431.2  = 1894.5783096 + 24.98584x + 545.8942159 - 25.98259 x

0.99675x = 9.2725255

:. x ~~ 9.3 %

And 21.01 - x = 11.71 %

Hence, the abundance of ""_12^25Mg is 9.3% and that of ""_12^26 Mg is 11.71%.

Concept: Atomic Masses and Composition of Nucleus
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#### APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 13 Nuclei
Exercise | Q 23 | Page 464

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