To find the percentage of the heavier isotope, we first need to determine the relative amounts of each isotope that gives the average atomic weight.

Let's denote the fraction of the lighter isotope (10.01 amu) as 'a' and the fraction of the heavier isotope (11.01 amu) as 'b'. Since these are the only two isotopes, a + b = 1.

The average atomic weight of the element is given by the sum of the weights of the isotopes, each multiplied by their respective fraction. So, 10.01a + 11.01b = 10.81.

We can now solve these two equations to find the values of 'a' and 'b'.

From a + b = 1, we can express 'a' as 1 - b. Substituting this into the second equation gives 10.01(1 - b) + 11.01b = 10.81.

Expanding and simplifying this equation gives 10.01 - 10.01b + 11.01b = 10.81, which simplifies further to 1.00b = 0.80.

Solving for 'b' gives b = 0.80, which means that 80% of the atoms are of the heavier isotope. So, Y = 80.

Question

To find the percentage of the heavier isotope, we first need to determine the relative amounts of each isotope that gives the average atomic weight.

Let's denote the fraction of the lighter isotope (10.01 amu) as 'a' and the fraction of the heavier isotope (11.01 amu) as 'b'. Since these are the only two isotopes, a + b = 1.

The average atomic weight of the element is given by the sum of the weights of the isotopes, each multiplied by their respective fraction. So, 10.01a + 11.01b = 10.81.

We can now solve these two equations to find the values of 'a' and 'b'.

From a + b = 1, we can express 'a' as 1 - b. Substituting this into the second equation gives 10.01(1 - b) + 11.01b = 10.81.

Expanding and simplifying this equation gives 10.01 - 10.01b + 11.01b = 10.81, which simplifies further to 1.00b = 0.80.

Solving for 'b' gives b = 0.80, which means that 80% of the atoms are of the heavier isotope. So, Y = 80.

Knowee AI · Accepted Answer

To find the percentage of the heavier isotope, we first need to determine the relative amounts of each isotope that gives the average atomic weight.

Let's denote the fraction of the lighter isotope (10.01 amu) as 'a' and the fraction of the heavier isotope (11.01 amu) as 'b'. Since these are the only two isotopes, a + b = 1.

The average atomic weight of the element is given by the sum of the weights of the isotopes, each multiplied by their respective fraction. So, 10.01a + 11.01b = 10.81.

We can now solve these two equations to find the values of 'a' and 'b'.

From a + b = 1, we can express 'a' as 1 - b. Substituting this into the second equation gives 10.01(1 - b) + 11.01b = 10.81.

Expanding and simplifying this equation gives 10.01 - 10.01b + 11.01b = 10.81, which simplifies further to 1.00b = 0.80.

Solving for 'b' gives b = 0.80, which means that 80% of the atoms are of the heavier isotope. So, Y = 80.

Naturally occurring element ‘X’ consists of two isotopes whose atomic weights are 10.01 amu and 11.01 amu. The average atomic weight of natural element ‘X’ is 10.81 amu. The percentage of heavier isotopes of element ‘X’ is Y. Find the value of

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