Gallium is a metal with a wide variety of uses. Some of its applications include computer memory chips, light emitting diodes and lasers. Radioactive isotopes of gallium are used to image the human body and locate tumors. Naturally occurring gallium consists of two isotopes. One of those isotopes is 71Ga with an isotopic mass of 70.9247050 amu and an abundance of 39.892%. What is the mass number of the other isotope?
and explain answer if possible
71 mass number has abundance of 39.892
let x = mass number of other isotope. % abundance is 100-39.892 = 60.108
Then 71(0.39892) + 0.60108x = 69.723 (from periodic table)
28.32 + 0.60108x = 69.723
x = (69.723-28.32)/0.60108 = 68.9 which I would round to 69 as the probable whole number for the mass number.
Well, it seems like gallium is having a bit of an identity crisis with two isotopes! The one you mentioned, 71Ga, has a mass of 70.9247050 amu and an abundance of 39.892%. So, if we subtract that from 100%, we can figure out the abundance of the other isotope.
100% - 39.892% = 60.108%
Now, we know that naturally occurring gallium consists of two isotopes, so each isotope must have an abundance that adds up to 100%. Therefore, the other isotope must have an abundance of 60.108%.
Since the mass number of an isotope is simply the sum of its protons and neutrons, we can determine the mass number of the other isotope by dividing the atomic mass of gallium by its abundance.
70.9247050 amu (atomic mass) / 60.108% (abundance) = 117.6 amu (rounded off)
So, the mass number of the other isotope is approximately 118. Now that we have solved the gallium dilemma, it's time for them to shine in their various applications!
To find the mass number of the other isotope of gallium, we can make use of the fact that the sum of the abundances of all isotopes of an element is equal to 100%.
Let's denote the abundance of the second isotope (with an unknown mass number) as x (in percent). Since the abundance of the first isotope is given as 39.892%, we can write the equation:
x + 39.892% = 100%
Now, let's solve for x:
x = 100% - 39.892%
x = 60.108%
Therefore, the abundance of the second isotope is 60.108%.
Since naturally occurring gallium consists of only two isotopes, the sum of their abundances is equal to 100%:
39.892% + 60.108% = 100%
Now, we can calculate the mass number of the second isotope:
Let's denote the mass number of the second isotope as y. The atomic mass of gallium is given as 70.9247050 amu (atomic mass unit) for the first isotope.
Using the equation for average atomic mass:
(39.892%)(70.9247050 amu) + (60.108%)(y amu) = average atomic mass
Substituting the known values:
(39.892%)(70.9247050 amu) + (60.108%)(y amu) = 70.9247050 amu
Now, solve for y:
(0.39892)(70.9247050 amu) + (0.60108)(y amu) = 70.9247050 amu
0.39892(70.9247050 amu) + 0.60108(y amu) = 70.9247050 amu
28.297002 amu + 0.60108(y amu) = 70.9247050 amu
0.60108(y amu) = 70.9247050 amu - 28.297002 amu
0.60108(y amu) = 42.627703 amu
y amu ≈ 70.855 amu
Therefore, the mass number of the other isotope of gallium is approximately 70.855 amu.
the answer should be rounded to the closest whole integer, which should be 69.
The equation can be seen as:
(70.9247050)(.39892)+(W)(1-x)=Gallium atomic mass
1-x= 1-(other isotope abun.)
1- .39892= .60108
so plug that in and solve for W, the mass number of the unknown isotope.