Gallium has an atomic mass of 69.7 amu. In a typical sample, 60.4% of Ga exxists as a Ga-69 (68.9257 amu). What isa the identity and the atomic mass of the other isotope?
Assume there are only two isotopes present. The average atomic mass is 69.7. If 60.4% is isotope Ga69, then 39.6% has a different mass, M. Solve this weighted-average-mass equation for M:
69.7 = (.604)(68.93) + (.396)M
.396M = 69.7 - 41.63 = 28.07
M = 70.87
That other isotope would probably be isotope Ga71.
A table of isotope abundances confirms this result
To find the identity and atomic mass of the other isotope of gallium, we can start by assuming that there are only two isotopes present in the typical sample of gallium. Let's call the atomic mass of the other isotope "x".
Given information:
- Atomic mass of Ga = 69.7 amu
- Percentage of Ga-69 = 60.4%
- Atomic mass of Ga-69 = 68.9257 amu
We can set up an equation using the average atomic mass of gallium:
Average atomic mass = (fraction of isotope 1 * atomic mass of isotope 1) + (fraction of isotope 2 * atomic mass of isotope 2)
The fraction of isotope 1 can be calculated by subtracting the percentage of isotope 2 from 100%:
Fraction of isotope 1 = 100% - Percentage of isotope 2
Fraction of isotope 1 = 100% - 60.4% = 39.6%
Now we can plug in the known values and solve for the atomic mass of the other isotope:
69.7 amu = (39.6/100 * 68.9257 amu) + (Percentage of isotope 2/100 * x amu)
Simplifying the equation:
69.7 = 27.2874712 + (Percentage of isotope 2/100 * x)
Rearranging the equation:
(Percentage of isotope 2/100 * x) = 69.7 - 27.2874712
(Percentage of isotope 2/100 * x) = 42.4125288
Now we can solve for the atomic mass of the other isotope, x:
(Percentage of isotope 2/100) * x = 42.4125288
Percentage of isotope 2 = 100% - 60.4% = 39.6%
(39.6/100) * x = 42.4125288
x = (42.4125288 * 100) / 39.6
x ≈ 107.2828283 amu
Therefore, the identity and atomic mass of the other isotope of gallium is Ga-107 (approximately 107.28 amu).
To find the identity and atomic mass of the other isotope of gallium, we can use the given information that 60.4% of gallium exists as Ga-69 (68.9257 amu).
Let's assume x is the abundance (in percentage) of the other isotope of gallium.
The sum of the abundances of both isotopes should equal 100%.
So, the abundance of the other isotope can be calculated as follows:
100% - 60.4% = 39.6% = x
Now we can set up an equation using the atomic masses of the isotopes to find the atomic mass of the other isotope.
(68.9257 amu * 60.4%) + (atomic mass of the other isotope * 39.6%) = 69.7 amu
(0.604 * 68.9257) + (0.396 * atomic mass of the other isotope) = 69.7
41.6506 + 0.396 * atomic mass of the other isotope = 69.7
0.396 * atomic mass of the other isotope = 69.7 - 41.6506
0.396 * atomic mass of the other isotope = 28.0494
Dividing both sides by 0.396:
atomic mass of the other isotope = 28.0494 / 0.396
Calculating the value:
atomic mass of the other isotope ≈ 70.8 amu
Therefore, the other isotope of gallium is Ga-70, and its atomic mass is approximately 70.8 amu.