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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?

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Eduard22sly

The mass of the other isotope is 68.9254620 amu.

Let the first isotope (⁷¹Ga) be A

Let the other isotope be B

Let the mass of the other isotope be y

From the question given above, the following data were obtained:

For A (isotope ⁷¹Ga):

Mass of A = 70.9247050 amu

Abundance (A%) = 39.892%

For B (the other isotope):

Abundance (B%) = 100 – 39.892

Abundance (B%) = 60.108%

Mass of B = y =?

Recall:

Atomic mass of gallium = 69.723

The mass of the other isotope can be obtained as illustrated below:

Atomic mass = [(mass of A × A%)/100] + [(mass of B × B%)/100]

69.723 = [(70.9247050 × 39.892)/100] + [(y × 60.108)/100]

69.723 = 28.2932833 + 0.60108y

Collect like terms

69.723 – 28.2932833 = 0.60108y

41.4297167 = 0.60108y

Divide both side by 0.60108

y = 41.4297167 / 0.60108

y = 68.9254620 amu

Therefore, the mass of the other isotope is 68.9254620 amu

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