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### Topic: %abundances of isotopes  (Read 1434 times)

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#### Joseph Palumbo

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##### %abundances of isotopes
« on: June 18, 2024, 08:10:04 PM »
In the book 'Chemistry an atoms based approach' , chapter 2 end of chapter problem 2.41,"Vanadium in nature consists of two isotopes: Vanadium-50 and Vanadium-51. Which is more abundant?"

Now I have: 50amu's*x+51amu's*(1-x)=avg amu's form periodic table
50x+51(1-x)=50.9414
50x+51-51x=50.9414
x(50-51)=50.9414-51
x=-.0586/(50-51)
x=-.0586/-1
.0586*10^2=5.86%
and if (1-x) is Vanadium-51 then
1-5.86%=-4.86
However from data sheets I see for Vanadium-50: .250% exact mass 49.946
for Vanadium-51: 99.750% exact mass 51.94

I do not understand this even though my calculations do show Vanadium-51 to be more % abundance it doen't look
doesn't match the data

#### Borek

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##### Re: %abundances of isotopes
« Reply #1 on: June 19, 2024, 02:58:43 AM »
You should use exact masses in calculations, not just 50 and 51.

Note: not 51.94, but 50.94 (actually, according to wikipedia page on vanadium isotopes,  50.9439595(11), the other number being 49.9471585(11)).

Try to redo the math using exact values and see what you get.

Also:

1-5.86%=-4.86

Not 1, but 100%.
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#### billnotgatez

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##### Re: %abundances of isotopes
« Reply #2 on: June 19, 2024, 11:24:12 PM »
@Joseph Palumbo
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