Question

The atomic mass of europium is 151.9 amu. There are two naturally occuring isotopes on europium, eu-151 with a mass of 151.0 amu and eu153 with a mass of 153.0. The percent natural abundance of the eu151 should be

Answer 1

The natural abundance of eu-153 is 45.0 %

The natural abundance of eu-151 is 55.0 %

Step-by-step explanation:

Step 1: Data given

The atomic mass of europium is 151.9 amu.

eu-151 hass with a mass of 151.0 amu

eu153 hass a mass of 153.0 amu

Step 2: Calculate the percent natural abundance

natural abundance eu-151 = X

natural abundance eu-153 = 1-X

151.9 = 151.0* X + 153.0 * (1-X)

151.9 = 151.0X + 153.0 -153.0 X

-1.1 = -2.0 X

X = 0.55 = 55 %

The natural abundance of eu-153 is 45.0 %

The natural abundance of eu-151 is 55.0 %

Answer 2

55%

Step-by-step explanation:

Let A represent isotope eu-151

Let B represent isotope eu-153

Let A% represent Abundance of isotope A (eu-151)

Let B represent abundance of isotope B (eu-153)

The abundance of isotope A (eu-151) can be obtained as follow:

Step 1:

Data obtained from the question include:

Atomic mass of Europium = 151.9 amu

Mass of isotope A (eu-151) = 151.0 amu

Mass of isotope B (eu-153) = 153.0

amu

Abundance of isotope A (eu-151) = A%

Abundance of B (eu-153) = B% = 100 - A%

Step 2:

Determination of the abundance of Abundance of isotope A (eu-151). This is illustrated below:

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

151.9 = [(151 x A%)/100] + [(153x B%)/100]

151.9 = [(151 x A%)/100] + [(153x (100-A%))/100]

151.9 = [151A%/100] + [15300 -

153A%/100]

151.9 = (151A% + 15300 - 153A%) /100

Cross multiply to express in linear form

151.9 x100 = 151A% + 15300 - 153A%

15190 = 151A% + 15300 - 153A%

Collect like terms

15190 - 15300= 151A% - 153A%

- 110 = - 2A%

Divide both side by - 2

A% = - 110 / - 2

A% = 55%

Therefore the abundance of eu-151 is 55%