Answer:
The percent abundances of the vanadium isotopes are 0.25% 50V and 99.75% 51V.
Explanation:
Let 50V be isotope A
Let 51V be isotope B
Mass number of isotope A (50V) = 49.9472
Mass number of isotope B (51V) = 50.9440
Abundance of isotope A (50V) = A%
Abundance of isotope B (51V) = B% = 100 — A
The atomic weight of vanadium
= 50.9415
Atomic weight = [(Mass of A x Abundance of A)/100] + [(Mass of B x Abundance of B) /100]
50.9415 = [(49.9472xA%)/100] + [(50.9440x(100 — A))/100]
50.9415 = [49.9472A%/100] + [(5094.40 — 50.9440A%)/100]
Multiply through by 100
5094.15 = 49.9472A% + 5094.40 — 50.9440A%
Collect like terms
5094.15 — 5094.40 = 49.9472A% — 50.9440A%
—0.25 = — 0.9968A%
Divide both side by — 0.9968
A% = —0.25/ — 0.9968
A% = 0.25%
B% = 100 — 0.25 = 99.75%
The percent abundances of the vanadium isotopes are 0.25% 50V and 99.75% 51V.
