Question

An element of atomic weight Z consists of two isotopes of mass number Z - 1 and Z + 2. Calculate the % of higher isotope.

Answer 1

Abundance of an isotope can be calculated as follows :

Let abundance of isotope with atomic mass Z+2 is x
Then abundance of isotope Z-1 is 1-x

(Z+2) x + (Z-1)(1-x) = Z
Solving we get
x=1/3
Therefore abundance of Z+2 is = (1/3)*100=33.33 %
And abundance of Z-1 is = 1-33.33 =67.66 %

Therefor isotope with atomic mass Z-1 is higher in % abundance

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Answer 2

To determine: The percentage of abundance of the higher isotope of the two "isotopes" of an "element".

Given Data: The weight of an element is Z

Mass number of two isotopes of the element are Z-1 and Z+2

Calculations:

Step 1: Assume abundance of isotope with mass number Z+2 is x

Therefore,  

Abundance of isotope with mass number Z-1 is 1-x

Step 2: Determine the value of x using the equation

$\left( Z+2 \right) x\quad +\quad \left( Z-1 \right) \left( 1-x \right) \quad =\quad Z$

Solving this we get

$x\quad =\quad \frac { 1 }{ 3 }$

Step 3: Substitute the value of x in abundance of the two isotopes separately to find which isotope is higher in abundance.

Abundance of $Z\quad +\quad 2\quad =\quad \frac { 1 }{ 3 } \quad \times \quad 100\quad =\quad 33.33%$

Abundance of $Z\quad -\quad 1\quad =\quad 1\quad -\quad 33.33\quad =\quad 67.66%$

Hence the percentage of abundance of the isotope Z-1 is higher than the other isotope.