Question

Nitrogen occurs in nature in the form of two isotopes with atomic mass 14 and 15 respectively .if average atomic mass of nitrogen is 14.0067.What is the percentage abundance of the two isotopes ?​

Answer 1

Answer:-

Let

• %abundance of N-14 isotope=x
• %abundance of N-15 isotope=100-x

ATQ,

The average atomic mass=14.0067

$\\ \sf\longmapsto \dfrac{14\times x+(100-x)15}{100}=14.0067$

$\\ \sf\longmapsto \dfrac{14x+(100-x)15}{100}=14.0067$

$\\ \sf\longmapsto \dfrac{14x+1500-15x}{100}=14.0067$

$\\ \sf\longmapsto -x+1500=1400.67$

$\\ \sf\longmapsto -x=1400.67-1500$

$\\ \sf\longmapsto -x=-99.33$

$\\ \sf\longmapsto x=99.33$

$\\ \sf\longmapsto 100-x=100-99.33=0.67$

Hence

$\\ \underline{\boxed{\bf{\therefore \%\:abundance\:of\:N-14 \:isotope\:is \:99.33\%.}}}$

$\\ \underline{\boxed{\bf{\therefore \%aboundance\:of\:N-15\:isotope\:is\:0.67\%.}}}$