Question

the atomic weight of copper is 63.546. There are only two naturally occurring isotopes of copper 63Cu and 65Cu. the natural occurring abundance of the 63Cu at the top must be approximately

Answer 1

let x = % abundance 63Cu
let y = % abundance 65Cu
x +y = 100
y = 100-x

63.546 = 62.9396 x + 64.9278 ( 100-x) / 100

6354.6 = 62.9396 x + 6492.78 - 64.9278 x

138.18 = 1.9882 x

x = 69.50 %
y = 100 - 69.50 = 30.50

Answer 2

Answer: The naturally occurring abundance for $_{29}^{63}\textrm{Cu}$ is 72.7 %.

Explanation:

Let us assume the fractional abundance for one of the isotopes is 'x'. So, the fractional abundance for another isotope will be (1 - x).

We are given:

Mass of $_{29}^{63}\textrm{Cu}$ = 63 amu

Fractional abundance of $_{29}^{63}\textrm{Cu}$ = x

Mass of $_{29}^{65}\textrm{Cu}$ = 65 amu

Fractional abundance of $_{29}^{65}\textrm{Cu}$ = (1-x)

Average atomic mass of copper = 63.546 amu

To calculate the fractional abundance for the isotopes, we use the equation:

$\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_i$

Putting values in above equation, we get:

$63.546=63(x)+65(1-x)\\\\x=0.727$

Percentage abundance for $_{29}^{63}\textrm{Cu}$ = 0.727 × 100 = 72.7 %

Hence, the naturally occurring abundance for $_{29}^{63}\textrm{Cu}$ is 72.7 %.