How to find the "a" and the "b"?

Question

10.81=a(10.01294) + b(11.00931)

In this question I have to find the abundance of Boron's two isotopes 10 and 11, so how to find the X?

10.81 is the average atomic mass of Boron.

Thank you!!

Answer 1

a+b=1 ?

=> a=1-b

=> (1-b) 10.01294 + b 11.00931 = 10.81

=> 0.99637 b = 0.79706

=> b = 0.8

So a = 0.2 and b = 0.8

in every sense b = 4a !

Answer 2

Hi,

Let x = decimal equal to the % of Boron 10 isotope and 1 - x = decimal equal to the % of Boron 11 isotope

x(10.01294) + (1 - x)(11.00931) = 10.81

10.01294x + 11.00931 - 11.00931x = 10.81

11.00931 - .99637x = 10.81

-.99637x = -.19931

x = .20 <==ANSWER

1 - x = .80 <==ANSWER

Boron 10 is about 20% and boron 11 is the other 80%. <==ANSWER

This can be verified at the following site:

From http://en.wikipedia.org/wiki/Boron

The 10B isotope is good at capturing thermal neutrons. Natural boron is about 20% 10B and 80%11B. The nuclear industry enriches natural boron to nearly pure 10B. The waste product, or depleted boron, is nearly pure 11B.

.20(10.01294) + .80(11.00931) = 10.810036

a = .20

b = .80

I hope that helps!! :-)

Answer 3

in this case a and b are percentages, so if we disregard other isotopes we'll assume a+b=1.

10.81=a(10.01294)+(1-a)(11.009310

10.81=11.009310-0.99637a

a=0.19931/0.99637=20%

b=1-a=80%

Answer 4

I do not see any X in that. How can one find x?

Regarding a and b there will be many many possibilities. and one of them has to be negative. What are possible values of a and b? I do not know why a= x and b =1-x. Is a+b =1?

Answer 5

10.81=a(10.01294) + b(11.00931)

a=x .... b= 1-x

x(10.01294) + (1-x)(11.00931)

10.01294x+11.00931-11.00931x = 10.81

-0,99637x+11.00931=10,81

-0,99637x = -0,19931

x = -0,19931/-0,99637 = 0.200

a=0.2    b= 0.8