10.01x +11.01(100-x) /100=10.81
10.01x +1101 - 11.01x =1081
x=20%

Naturally Occurring Boron Isotopes

Isotopes and Atomic Weights

Boron, with atomic number 5, has two naturally occurring isotopes: boron-10 (^10B) and boron-11 (^11B). These isotopes have atomic weights of 10.01 and 11.01, respectively.

Atomic Weight of Natural Boron

The atomic weight of natural boron can be calculated as the weighted average of the atomic weights of its isotopes, taking into account their abundances. The atomic weight of natural boron is given as 10.81.

Percentage of Each Isotope

To determine the percentage of each isotope in natural boron, we can set up a system of equations. Let x represent the abundance (percentage) of ^10B and y represent the abundance (percentage) of ^11B. We know that the sum of the abundances should be 100%:

x + y = 100

We also know that the atomic weight of natural boron is the weighted average of the isotopes' atomic weights:

(x * 10.01) + (y * 11.01) = 10.81

Solving the Equations

We can solve this system of equations using substitution or elimination. Let's use substitution to solve for x:

From the first equation, we have x = 100 - y.

Substituting this into the second equation:

((100 - y) * 10.01) + (y * 11.01) = 10.81
1000.1 - 10.01y + 11.01y = 10.81
1000.1 + 0.1y = 10.81
0.1y = 10.81 - 1000.1
0.1y = -989.29
y = -989.29 / 0.1
y = -9892.9

This solution yields a negative value for y, which is not physically meaningful. It indicates that the given atomic weight of natural boron is not consistent with the given isotopic atomic weights. Therefore, the problem might contain an error or inconsistency.

Conclusion

In conclusion, based on the given information, it is not possible to determine the percentage of each isotope in natural boron. The given atomic weight of natural boron is not consistent with the atomic weights of its isotopes. Further clarification or correction of the information provided is necessary to accurately determine the percentage abundances of ^10B and ^11B in natural boron.