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jekas [21]
3 years ago
13

Rubidium is comprised of two isotopes, one of which has a natural abundance of 72% and contains 48 neutrons in the nucleus. give

n that the calculated atomic mass for rubidium is 85.5, how many neutrons are contained in the nucleus of an atom of the second isotope?
Chemistry
1 answer:
SOVA2 [1]3 years ago
6 0
Since there are only two isotopes, then that means the other isotope has an abundance of: 100 - 72 = 28%. Let y be the mass of the first isotope, and x be the mass of the second. The equation would be

85.5 = 0.72y + 0.28x

Now, rubidium has 37 protons, and each proton has a mass of 1.00727647 amu. When neutral, it must also have 37 electrons in which each electron weighs 0.000548597 amu. Let n be the number of neutrons, in which each neutron weighs <span>1.008664 amu. The solution is as follows:

y = 37(</span>1.00727647) + 37(0.000548597) + 48(1.008664)
y = 85.7054 amu

Then, x would be:
85.5 = 0.72(85.7054) + 0.28x
x = 84.972 amu
So,
x = 84.972 = 37(1.00727647) + 37(0.000548597) + n(1.008664)
Solving for n,
n = 47.27 ~ 47

<em>Therefore, there are 47 neutrons in the second isotope.</em>
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