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An element with atomic mass Z consists of two isotopes of mass number Z - 1 and Z+ 2. The percentage abundance of the heavier isotope is (up to one place of the decimal):
Correct answer is '33.3'. Can you explain this answer?
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An element with atomic mass Zconsists of two isotopes of mass number Z...
The atomic mass of element = Z
Two isotopes have mass number 
We have to find the percentage abundance of heavier isotope (z+2)
Let the percentage abundance of an isotope with mass number z+2 be y
The percentage abundance isotope with mass number z-1 is (100+y)
We know that, (Percentage abundance of isotope I x Mass number if isotopes I) + (Percentage abundance of isotope II x Mass number of isotope II)− Mass number of Z x 100
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An element with atomic mass Zconsists of two isotopes of mass number Z...
Given Information:
- Atomic mass of element = Z
- Isotopes with mass numbers Z - 1 and Z + 2
- Percentage abundance of heavier isotope = 33.3%
Solution:
Step 1: Setting up the equation
Let x be the percentage abundance of the lighter isotope (mass number Z - 1).
Since the total abundance of both isotopes is 100%, we can write:
x + 33.3% = 100%
x = 100% - 33.3%
x = 66.7%
Step 2: Calculating average atomic mass
Average atomic mass = (abundance of isotope 1 * mass of isotope 1) + (abundance of isotope 2 * mass of isotope 2)
Average atomic mass = (66.7% * (Z - 1)) + (33.3% * (Z + 2))
Average atomic mass = 0.667Z - 0.667 + 0.333Z + 0.666
Average atomic mass = Z
Step 3: Finding the percentage abundance of the heavier isotope
Since the average atomic mass is Z, the percentage abundance of the heavier isotope (Z + 2) is equal to the difference between the average atomic mass and the mass of the lighter isotope (Z - 1).
Percentage abundance of heavier isotope = ((Z - 1) / ((Z + 2) - (Z - 1))) * 100%
Percentage abundance of heavier isotope = 33.3%
Therefore, the percentage abundance of the heavier isotope is 33.3%.
- Atomic mass of element = Z
- Isotopes with mass numbers Z - 1 and Z + 2
- Percentage abundance of heavier isotope = 33.3%
Solution:
Step 1: Setting up the equation
Let x be the percentage abundance of the lighter isotope (mass number Z - 1).
Since the total abundance of both isotopes is 100%, we can write:
x + 33.3% = 100%
x = 100% - 33.3%
x = 66.7%
Step 2: Calculating average atomic mass
Average atomic mass = (abundance of isotope 1 * mass of isotope 1) + (abundance of isotope 2 * mass of isotope 2)
Average atomic mass = (66.7% * (Z - 1)) + (33.3% * (Z + 2))
Average atomic mass = 0.667Z - 0.667 + 0.333Z + 0.666
Average atomic mass = Z
Step 3: Finding the percentage abundance of the heavier isotope
Since the average atomic mass is Z, the percentage abundance of the heavier isotope (Z + 2) is equal to the difference between the average atomic mass and the mass of the lighter isotope (Z - 1).
Percentage abundance of heavier isotope = ((Z - 1) / ((Z + 2) - (Z - 1))) * 100%
Percentage abundance of heavier isotope = 33.3%
Therefore, the percentage abundance of the heavier isotope is 33.3%.
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An element with atomic mass Zconsists of two isotopes of mass number Z - 1 and Z+ 2.The percentage abundance of the heavier isotope is (up toone place of the decimal):Correct answer is '33.3'. Can you explain this answer?
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