Bromine has two naturally occurring isotopes. Bromine-79 has a mass of 78.918 amu (atomic mass unit) and is 50.69% abundant. Using the atomic mass reported on the periodic table, determine the mass of bromine-81, the other isotope of bromine.
http://www.jiskha.com/display.cgi?id=1385001007
To determine the mass of bromine-81, we need to use the information provided about the abundance and atomic mass of bromine-79.
Let's start by calculating the mass contribution of bromine-79:
Mass of bromine-79 = 78.918 amu
Abundance of bromine-79 = 50.69%
Next, we need to find the mass contribution of all the other isotopes of bromine (which includes bromine-81) using the atomic mass reported on the periodic table. Let's assume the atomic mass reported on the periodic table is X.
Mass contribution of all other isotopes = (100% - abundance of bromine-79) * X
Since bromine has only two naturally occurring isotopes (bromine-79 and bromine-81), the mass contribution of bromine-81 will be the mass contribution of all other isotopes.
Now, we can set up an equation:
Mass contribution of bromine-81 = Mass contribution of all other isotopes
Mass contribution of bromine-81 = (100% - 50.69%) * X
Mass contribution of bromine-81 = 49.31% * X
The atomic mass of an element is the weighted average of the masses of its isotopes. Therefore, we can equate the mass contribution of bromine-81 to its atomic mass:
Mass of bromine-81 = 49.31% * X
To find X, we can set up another equation:
Atomic mass of bromine = (mass contribution of bromine-79) + (mass contribution of bromine-81)
Atomic mass of bromine = 50.69% * 78.918 amu + 49.31% * X
Now, we can rearrange the equation to solve for X:
X = (Atomic mass of bromine - 50.69% * 78.918 amu) / 49.31%
Substituting the values, we get:
X = (79.904 amu - 50.69% * 78.918 amu) / 49.31%
Now, we can substitute the calculated value of X into the equation we set up earlier to find the mass of bromine-81:
Mass of bromine-81 = 49.31% * X
Calculating this value will give us the mass of bromine-81.
To determine the mass of Bromine-81, we can use the information given about Bromine-79 and its abundance.
1. Let's assume the atomic mass of Bromine is given as X amu on the periodic table.
- Bromine-79 has a mass of 78.918 amu and is 50.69% abundant.
- The remaining isotope, Bromine-81, will have a mass of (X - Bromine-79's mass).
2. We know that the total abundance of isotopes is equal to 100%.
- The abundance of Bromine-79 is 50.69%.
- Therefore, the abundance of Bromine-81 will be (100% - 50.69%) or 49.31%.
3. We can now set up an equation to solve for X (the atomic mass of Bromine):
(Mass of Bromine-79 * Abundance of Bromine-79) + (Mass of Bromine-81 * Abundance of Bromine-81) = X
Plugging in the given values:
(78.918 amu * 0.5069) + (Mass of Bromine-81 * 0.4931) = X
4. Rearranging the equation to solve for Mass of Bromine-81:
Mass of Bromine-81 = (X - (78.918 amu * 0.5069)) / 0.4931
5. Finally, we can substitute the value of X (atomic mass of Bromine) from the periodic table to find the mass of Bromine-81.
Please note that the atomic mass of Bromine might vary slightly depending on the source or periodic table version.