Finding the Specific Activity of Rubidium Chloride

[Phillyfan321]

Homework Statement

The element rubidium consists of two isotopes, the stable 85Rb and radioactive 87Rb (abundance 27.83%). What is the specific activity of natural rubidium chloride? Use Ar85.47 gmol-1 for rubidium element, Ar 86.91 gmol-1 for 87Rb, and Mr 120.92 gmol-1 for RbCl.

Homework Equations

A2 = (λ2A1 /λ2-λ1) (e^-λ2 *t)
M = (N#/ avag const)* Ar

The Attempt at a Solution

I tried to convert 1g (subjective choice) of RbCl to 5 x 10^21 molecules, then apply percent abundance to get 1.4 x 10^21 Rb87. I converted that back to grams and got .2. I really don't know if I am on the right track or not, because I can't seem to figure out where I am going with this and if I need the other Ar value. Thanks.

 

[haruspex]

Homework Statement

The element rubidium consists of two isotopes, the stable 85Rb and radioactive 87Rb (abundance 27.83%). What is the specific activity of natural rubidium chloride? Use Ar85.47 gmol-1 for rubidium element, Ar 86.91 gmol-1 for 87Rb, and Mr 120.92 gmol-1 for RbCl.

Homework Equations

A2 = (λ2A1 /λ2-λ1) (e^-λ2 *t)
M = (N#/ avag const)* Ar

The Attempt at a Solution

I tried to convert 1g (subjective choice) of RbCl to 5 x 10^21 molecules, then apply percent abundance to get 1.4 x 10^21 Rb87. I converted that back to grams and got .2. I really don't know if I am on the right track or not, because I can't seem to figure out where I am going with this and if I need the other Ar value. Thanks.

Since this is not a chemistry forum, you will need to phrase your question in a way that assumes little knowledge of chemistry.

 

[Phillyfan321]

Well... Specific Activity in this case is Bq per unit mass (Disintegration/sg) which is what I need to find. Only part (28%) of the total compound is radioactive but when I thought of doing a sum for the components the stable isotope doesn't have a decay factor so I ran into a wall.

 

[haruspex]

Well... Specific Activity in this case is Bq per unit mass (Disintegration/sg) which is what I need to find. Only part (28%) of the total compound is radioactive but when I thought of doing a sum for the components the stable isotope doesn't have a decay factor so I ran into a wall.

Doesn't help me. E.g. what are Ar and Mr?

 

[HalfLostAndSearching]

I would approach this problem by first understanding the concept of specific activity. Specific activity is a measure of the amount of radioactive material present in a sample, and is defined as the activity per unit mass of the sample. In this case, we are trying to find the specific activity of natural rubidium chloride, which contains both stable 85Rb and radioactive 87Rb.

To find the specific activity, we can use the equation A/M, where A is the activity (in becquerels) and M is the mass of the sample (in grams). In order to use this equation, we need to first calculate the activity of both 85Rb and 87Rb separately.

The activity of a radioactive isotope can be calculated using the equation A = λN, where λ is the decay constant and N is the number of atoms of the isotope present. We can find the value of λ by using the half-life of the isotope, which is given as 49.5 days for 87Rb. This gives us a decay constant of 0.014, which can be converted to units of s^-1.

Next, we need to find the number of atoms of each isotope present in 1g of RbCl. We can do this by using the Avogadro's constant and the atomic weight of each isotope. For 85Rb, we have (1g/85.47 g/mol)*(6.022 x 10^23 atoms/mol) = 7.05 x 10^21 atoms. Similarly, for 87Rb, we have (0.2783g/86.91 g/mol)*(6.022 x 10^23 atoms/mol) = 2.42 x 10^21 atoms.

Now, we can calculate the activity of each isotope by multiplying the number of atoms by the decay constant. For 85Rb, this gives us an activity of 9.87 x 10^19 Bq, and for 87Rb, it gives us an activity of 3.39 x 10^19 Bq.

Finally, we can calculate the specific activity by dividing the activity by the mass of the sample. This gives us a specific activity for 85Rb of 9.87 x 10^19 Bq/g and for 87Rb of 1.13 x 10^