Need Help on Isotopes: Find Mass Number of Antimony

[allie2032]

Homework Statement

I have been working on this for ages and can't work it out.
Naturally occurring antimony (Sb) has a molar mass of 121.84 g/mol and contains only two isotopes. One is 121Sb which is 57.3% abundant. What is the mass number of the other isotope of naturally occurring antimony?

I have been through all my textbooks and can't find the answer, have also googled and I am totally stuck. I need to show how I came to my answer. I don't need to have the question done for me just how to go about working it out.
Thanks in advance for any help.

Homework Equations

The Attempt at a Solution

 

[phyzguy]

The molar mass is the average mass of all of the isotopes. If 57% is 121, what must the other one isotope be in order for the average to be 121.84?

 

[epenguin]

Yes, it's got to be a small whole number, now just over 40% if this other isotope adds 0.84 to the average, I think I can work out what it must be in my head, and if not just try 1, 2, 3,... you will never have to go very far.

 

[Cilabitaon]

Yes, it's got to be a small whole number, now just over 40% if this other isotope adds 0.84 to the average, I think I can work out what it must be in my head, and if not just try 1, 2, 3,... you will never have to go very far.

I don't follow your reasoning; the number must be greater than 121 for the average to be 0.84 higher with a lower abundance. I may just be misunderstanding, so sorry=]

allie, I'll assume you know how to take the average mass of two isotopes, but you may not have looked at the full equation for the mass; maybe this'll help :)

in this case $$\frac{(121 \times 57.3) + (M \times (100-57.3))}{100} = 121.84$$

 

[DeeNos]

First, we need to understand what isotopes are. Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. This means that they have the same atomic number, but different mass numbers. The mass number is the sum of the number of protons and neutrons in an atom's nucleus.

In this case, we are looking for the mass number of the other isotope of naturally occurring antimony. To find this, we can use the following formula:

Mass number = Atomic number + Number of neutrons

We know that antimony (Sb) has an atomic number of 51, which means it has 51 protons. We also know that the molar mass of antimony is 121.84 g/mol, which is the average mass of all the isotopes of antimony.

Since we are given that 121Sb is 57.3% abundant, this means that the other isotope must make up the remaining 42.7%. We can set up the following equation to solve for the mass number of the other isotope:

(0.427)x + (0.573)(121) = 121.84

Where x represents the mass number of the other isotope. Solving for x, we get:

x = (121.84 - 65.61)/0.427 = 105.36

Therefore, the other isotope of naturally occurring antimony has a mass number of 105.36. This means that it has 105 neutrons, since the atomic number (51) is the same for both isotopes.

To summarize, to find the mass number of the other isotope of antimony, we used the fact that the molar mass is the average of all the isotopes, and we set up an equation using the abundance of the two isotopes to solve for the mass number of the other isotope. I hope this helps in your understanding of isotopes and how to find the mass number.