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Copper is made of two isotopes. Copper-63 is 69.17% abundant and it has a mass of 62.9296 amu. Copper-65 is 30.83% abundant and it has a mass of 64.9278 amu. What is the weighted average mass of these two isotopes? Show your work. 

Sagot :

Alex19
The weighted atomic mass of these two isotopes is 63.5679 amu. To calculate this first multiply Copper-63's mass of 62.9296 amu by .6917 which gets you 43.5284. Then multiply Copper-65's mass of 64.9278 by .3083 which gets you 20.0395. Then add 43.5284 and 20.0395 to get the final answer of 63.5679 amu.

Answer: The average atomic mass of copper is 65.5456 amu.

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:

[tex]\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_i[/tex]    .....(1)

  • For [tex]_{29}^{63}\textrm{Cu}[/tex] isotope:

Mass of [tex]_{29}^{63}\textrm{Cu}[/tex] isotope = 62.9296 amu

Percentage abundance of [tex]_{29}^{63}\textrm{Cu}[/tex] isotope = 69.17 %

Fractional abundance of [tex]_{29}^{63}\textrm{Cu}[/tex] isotope = 0.6917

  • For [tex]_{29}^{65}\textrm{Cu}[/tex] isotope:

Mass of [tex]_{29}^{65}\textrm{Cu}[/tex] isotope = 64.9278 amu

Percentage abundance of [tex]_{29}^{65}\textrm{Cu}[/tex] isotope = 30.83%

Fractional abundance of [tex]_{29}^{65}\textrm{Cu}[/tex] isotope = 0.3083

Putting values in equation 1, we get:

[tex]\text{Average atomic mass of copper}=[(62.9296\times 0.6917)+(64.9278\times 0.3083)][/tex]

[tex]\text{Average atomic mass of copper}=63.5456amu[/tex]

Thus, the average atomic mass of copper is 65.5456 amu.

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