Question

Nitrogen occurs in nature in the form of two isotopes with atomic mass 14 & 15 respectively. If average atomic mass of nitrogen is 14.0067, what is the % abundance of the isotopes?

Answer 1

Explanation:

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 % abundabce of the two isotopes ? % abundance of N-15 isotope = 0.67 %.

Answer 2

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

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

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