(a) Two stable isotope of `._3Li^6` and `._3Li^7` have respective abundances of `7.5%` and `92.5%`. These isotopes have masses 6.01512 and 7.01600 u respectively. Find the atomic weight of lithium.
(b) Boron has two stable isotopes `._5B^(10)` and `._5B^(11)`. Their respective masses are 10.01294 u and 11.00931 u, and the atomic weight of boron is 10.81 u. Find the abundances of `._5B^(10)` and `._5B^(11)`.

Explanation

Given,
Atomic mass of `""_(3)Li^(6) = 6.01512 u`
Atomic mass of `""_(3)Li^(7)= 7.01600`u
Abundance of `""_(3)Li^(6) = 7.5%`
Abundance of `""_(3)Li^(7)= 92.5%`
`therefore` Atomic mass of lithium is
`m(Li) -(7.5 xx 6.01512 + 92.5 xx 7.01600)/100` v
`=(45.1134 + 648.98)/100 u = 6.941 u`
(ii) Given, mass of `""_(5)B^(10) = 10.01294`u
Mass of `""_(5)B^(11) = 11.00931`u
Atomic massof boron, m(B) = 10.811 u
Let relative abundance of `""_(6)B^(10)` be x%
`therefore` Abundance of `""_(5)B^(11) = (100-x)%`
Now, atomic weight is given by
`m(B) = (x xx 10.01294 + (100-x) 11.00931)/100` u
`rArr x=19.831/0.99637 = 19.9%`
`therefore` Abundance of `""_(5)B^(10) = 19.9%`
And abundance of `""_(5)B^(11) = 100-19.9 = 80.1%`