Respuesta :
Answer:
The fractional abundance of the lighter isotope = 0.5185
Explanation:
Let y be the fractional abundance of the lighter isotope
Since total abundance = 100% = 1
Therefore the fractional abundance of heavier isotope = 1 - y
Average atomic mass = sum of isotopic mass * fractional abundance of each isotope
108.9047 (1 - y) + 106.90509 (y) = 107.868 2
108.9047 - 108.9047y + 106.90509y = 107.868
- 108.9047y + 106.90509y = - 108.9047 + 107.868
- 1.99961y = - 1.0367
y = (-1.0367)/(-1.9996)
y = 0.5185
Therefore, the fractional abundance of the lighter isotope = 0.5185
The fractional abundance of the lighter of the two isotopes is 0.5185. Thus, option D is correct.
The total abundance of the metal has been 100%. The total abundance of both heavier and lighter particles has been 1.
Suppose the abundance of the heavier particle is a.
The abundance of the lighter particle will be = 1-a.
The atomic mass of the element with isotopes can be calculated as:
Average atomic mass = Mass of isotope 1 [tex]\times[/tex] Abundance + Mass of isotope 2
The given average atomic mass = 107.8682 amu
The mass of lighter isotope 1 = 106.90509 amu
The mass of the heavier isotope = 108.9047 amu.
Substituting the values:
107.8682 = 106.90509 (1 - a) + 108.9047a
107.8682 = 106.90509 - 106.90509a + 108.9047a
107.8682 - 106.90509 = 1.99961a
0.96311 = 1.99961a
a = 0.48
a = abundance of the heavier particle
Thus, the abundance of heavier particle = 0.48
The abundance of lighter particle = 1 - a
The abundance of lighter particle = 1 - 0.48
The abundance of lighter particle = 0.518
The percent abundance of the lighter particle = 51.8%.
The fractional abundance of the lighter of the two isotopes is 0.5185. Thus, option D is correct.
For more information about the percent abundance, refer to the link:
https://brainly.com/question/14767342
