(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

(a) Mass of lithium isotope `_(3)^(6)Li, m_(1)= 6.01512" "u`
Mass of lithium isotope `""_(3)^(7)Li, m_(2)= 7.01600" "u`
Abundance of `_(3)^(6)Li, eta_(1)= 7.5%`
`_(3)^(7)Li, eta_(2)= 92.5%`
The atomic mass of lithium atom is given as:
`m=(m_(1)eta_(1)+m_(2)eta_(2))/(eta_(1)+eta_(2))`
`=(6.01512xx7.5+7.01600xx92.5)/(92.5+7.5)`
`=6.940934" "u`
(b) Mass of boron isotope `_(5)^(10)B,m_(1)=10.01294" "u`
Mass of boron isotope `_(5)^(11)B,m_(2)=11.00931" "u`
Abundance of `_(5)^(10)B,mu_(1)=x%`
Abundance of `_(5)^(11)B,mu_(2)=(100-x)%`
Atomic mass of boron, `m=10.811" "u`
The atomic mass of boron atom is given as:
`m=(m_(1)eta_(1)+m_(2)eta_(2))/(eta_(1)+eta_(2))`
`10.811=(10.01294xxx+11.00931xx(100-x))/(x+100-x)`
`therefore x=(19.821)/(0.99637)=19.89%`
And `100-x=80.11`
Hence, the abundance of `_(5)^(10)B" is "19.89%` and that of `_(5)^(11)B" is "80.11%`