Question

Copper exists naturally as two isotopes copper-63 with a mass of 62.93 amu and copper-65 with a mass of 64.93 amu. The average mass of copper is 63.55 amu. What is the approximate abundance of copper-63 in nature?

Answer 1

Answer: The percentage abundance of
`_(29)^(63)\textrm{Cu}` isotope is 69 %.

Step-by-step explanation:

Average atomic mass of an element is defined as the sum of masses of each isotope each multiplied by their natural fractional abundance.

Formula used to calculate average atomic mass follows:

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

We are given:

Let the fractional abundance of
`_(29)^(63)\textrm{Cu}` isotope be 'x'

• For
  `_(29)^(63)\textrm{Cu}` isotope:

Mass of
`_(29)^(63)\textrm{Cu}` isotope = 62.93 amu

Fractional abundance of
`_(29)^(63)\textrm{Cu}` isotope = x

• For
  `_(29)^(65)\textrm{Cu}` isotope:

Mass of
`_(29)^(65)\textrm{Cu}` isotope = 64.93 amu

Fractional abundance of
`_(29)^(63)\textrm{Cu}` isotope = (1-x)

• Average atomic mass of copper = 63.55 amu

Putting values in above equation, we get:

`63.55=[(62.93* x)+(64.93* (1-x))]\\\\x=0.69`

Converting this fractional abundance into percentage abundance by multiplying it by 100, we get:

`\Rightarrow 0.69* 100=69\%`

Hence, the percentage abundance of
`_(29)^(63)\textrm{Cu}` isotope is 69 %.