Question

${\large{\pmb{\sf{\underline{Hello \: Viewers!!}}}}}$

$\red{\bigstar}\:{\large{\pmb{\sf{\underline{A \: chemistry \: question...}}}}}$

1) The average atomic mass of a sample of an element ${\sf{X}}$ is ${\sf{16.2 \: u}}$ What are the percentage of isotopes ${\sf{{}^{16}_{ \: \: 8}X}}$ and ${\sf{{}^{18}_{ \: \: 8}X}}$ in the sample?

$\red{\bigstar}\:{\large{\pmb{\sf{\underline{Remember...}}}}}$

• "Please" don't spam!

• "Please" give answers by following all the rules of Brainly means no copy-paste, pilgrimage not allowed or else!

• Thank you for answer in advance! :) But I need answer, don't take thank before answering properly with explaination! ​

Answer 1

Given :

$\sf The \: average \: atomic \: mass \: of \: a \: sample \\ \sf \:of \: an \: element \: is \: {\sf{X}} \: is \: {\sf\red{16.2 \: u}}$

To find :

$\sf What \: are \: the \: percentage \: of \: isotopes \: {\sf{{}^{16}_{ \: \: 8}X}}$ and ${\sf{{}^{18}_{ \: \: 8}X}} \sf \: in \: the \: sample?$

Solution :

Let us , take

$\sf \red {The \: average \: atomic \: mass \: of \: a \: sample \: \green{X = 16.2 u.}}$

$\sf Let \: the \: percent \: of \: isotope \: of \: {\sf{{}^{16}_{ \: \: 8}X}} \: H \: be \: y \: and \: percent \: of \: isotope \: of \: y \red \{= (100 – y)%}$

$\sf18 \times \frac{Y}{100} + 16 \times \frac{(100 - Y)}{100} \green{= 16.2}$

$\sf \frac{18 \: Y}{100} + \frac{16(100 - Y)}{100} \red{ = 16.2}$

$\sf \: 18y + 1600 = 16y = 1620$

$\sf \: 2y \: = 1620 – 1600$

$\sf ∴ 2y = 20$

$\sf y = 10$

$\sf Percentage \: of \: isotope \: X \red{= 10 \: percent }$

$\sf Percentage \: of \: isotope \: \green y = 100 - 10 = 90%.$

Therefore, the percentage will be got 90%

Answer 2

$\underline{\orange{\sf{Given:-}}}$

We are given that, average atomic mass of a sample of X is 16.2 u.

$\underline{\orange{\sf{To\:Find:-}}}$

We need to find the percentage of the following isotopes:

$\tt{\implies ^{16}_8X}$

$\tt{\implies ^{18}_8X}$

$\underline{\orange{\sf{Assumptions:-}}}$

Let:

$\tt{\implies Percentage\:of\:^{18}_8X = a}$

Then, we know that:

$\tt{\implies Percentage\:of\:^{18}_8X+Percentage\:of\:^{16}_8X = 100}$

$\tt{\implies a+Percentage\:of\:^{16}_8X = 100}$

$\tt{\implies Percentage\:of\:^{16}_8X = 100-a}$

$\underline{\orange{\sf{Solution:-}}}$

To find the average atomic mass, we use the formula:

$\tt{\implies \dfrac{Atomic\:mass\:of\:^{18}_8X \times Percentage\:of\:^{18}_8X+Atomic\:mass\:of\:^{16}_8X \times Percentage\:of\:^{16}_8X}{100}}$

$\tt{\implies \dfrac{18a+16(100-a)}{100} = 16.2}$

$\tt{\implies \dfrac{18a+1600-16a}{100} = 16.2}$

$\tt{\implies \dfrac{2a+1600}{100} = 16.2}$

On cross multiplying the equation, we get:

$\tt{\implies 2a+1600 = 100 \times 16.2}$

$\tt{\implies 2a+1600 = 1620}$

$\tt{\implies 2a = 1620-1600}$

$\tt{\implies 2a = 20}$

$\tt{\implies a = \dfrac{20}{2}}$

$\tt{\implies a = 10}$

$\underline{\orange{\sf{Conclusion:-}}}$

$\tt{\implies Percentage\:of\:^{18}_8X = 10}$

$\tt{\implies Percentage\:of\:^{16}_8X = 100-10 = 90}$

Hence, the percentage of the isotopes are 90% and 10% respectively.