katherynbanks
Answered

the atomic mass of element A is 63.6 atomic mass units. the only naturally occurring isotopes of element A are A-63 and A-65. the percent abundances in a naturally occurring sample of element A are closest to
A) 31% A-63 and 69% -65
B) 69%A-63 and 31% A-65
C) 50% A-63 and 50% A-65
D) 100% A-63 and 0% A-65

Verified Answer :

tayjay99

This question uses weighted averages.

Since the average mass of element A is 63.6 amu and the only two isotopes are 63 and 65, 

63.6 = x% 63 + (1-x%) 65

If you don't want to calculate this (like me), you can look at the answer choices.

If it was 100% A-63, the weight would be 63. Cross off D.
If it was 50/50, the weight would be 64. Cross off C.
So since the weighted average is 63.6, you would expect there to be more A-63 than A-65, so B is the only answer that makes sense.

okpalawalter8

We have that   the percent abundances in a naturally occurring sample of element is closest to

50% A-63 and 50% A-65

Option C


From the question we are told

the atomic mass of element A is 63.6 atomic mass units. the only naturally occurring isotopes of element A are A-63 and A-65. the percent abundances in a naturally occurring sample of element A are closest to

A) 31% A-63 and 69% -65

B) 69%A-63 and 31% A-65

C) 50% A-63 and 50% A-65

D) 100% A-63 and 0% A-65


Generally the equation for the Atomic mass avg  is mathematically given as

Avg M=\frac{mass of isotope * abundance}{abundance}

Therefore

63.6=\frac{(\63a+65(100-a)}{x+100-x}

63.6=\frac{63a+6500-65a}{100}

63.6=\frac{-3a+6500}{100}

6360=-3a+6500

6360-6500=-3a

a=46.67

Therefore

 the percent abundances in a naturally occurring sample of element A are

46.67\% and 53.3\% respectively

Therefore it is closest to

50% A-63 and 50% A-65

Option C


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