Question

An element Z contains two naturally occuring isotopes 35/17 Z and 37/17 Z. If the average atomicity mass of this element be 35.5 u. Calculate the percentage of two isotopes.

Answer 1

Answer: The percentage of one isotope is coming out to be 75% and the percentage of other isotope is coming out to be 25%.

Explanation:

It is given that, an element has 2 isotopes. Let the fractional abundance of first isotope be 'x', so the fractional abundance for another isotope will be '(1 - x)' because the total fractional abundance is always equal to 1.

For isotope 1, which is $_{17}^{35}\textrm{Z}$:

Mass of this isotope = 35 u

Fractional abundance = x

For isotope 2, $_{17}^{37}\textrm{Z}$:

Mass of this isotope = 37 u

Fractional abundance = 1 - x

Average atomic mass of element Z = 35.5 u

Expression for the average atomic mass of an element is given by the equation:

$\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_i$

Putting values in above equation, we get:

$35.5=[(35\times x)+37(1-x)]\\\\1.5=2x\\\\x=0.75$

Fractional abundance of isotope 1 = x = 0.75

Percentage abundance of isotope 1 = $0.75\times100=75\%$

Fractional abundance of isotope 2 = 1 - x = (1 - 0.75) = 0.25

Percentage abundance of isotope 2 = $0.25\times100=25\%$

Hence, the percentage of one isotope is coming out to be 75% and the percentage of other isotope is coming out to be 25%.

Answer 2

Answer:

The percentage of one isotope is coming out to be 75% and the percentage of other isotope is coming out to be 25%.

Explanation:

It is given that, an element has 2 isotopes. Let the fractional abundance of first isotope be 'x', so the fractional abundance for another isotope will be '(1 - x)' because the total fractional abundance is always equal to 1.

For isotope 1, which is :

Mass of this isotope = 35 u

Fractional abundance = x

For isotope 2, :

Mass of this isotope = 37 u

Fractional abundance = 1 - x

Average atomic mass of element Z = 35.5 u

Expression for the average atomic mass of an element is given by the equation:

Putting values in above equation, we get:

Fractional abundance of isotope 1 = x = 0.75

Percentage abundance of isotope 1 =

Fractional abundance of isotope 2 = 1 - x = (1 - 0.75) = 0.25

Percentage abundance of isotope 2 =

Hence, the percentage of one isotope is coming out to be 75% and the percentage of other isotope is coming out to be 25%.

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