Question

solve the question below. (1 point) naturally occurring europium (eu) consists of two isotopes was a mass of 151 and 153. if the average atomic mass of europium is 151.97 amu, what are the abundances of each individual isotope? eu - 151: 51.5% eu - 153: 48.5% eu - 151: 48.5% eu - 153: 51.5% eu - 151: 55.4% eu - 153: 44.6% eu - 151: 44.6% eu - 153: 55.4%

Explanation:

Step1: Let the abundance of Eu - 151 be $x$, then the abundance of Eu - 153 is $1 - x$.

The formula for average atomic mass is $m_{avg}=m_1\times x_1 + m_2\times x_2$. Here, $m_1 = 151$, $m_2=153$, $x_1=x$, $x_2 = 1 - x$ and $m_{avg}=151.97$. So we have the equation $151x+153(1 - x)=151.97$.

Step2: Expand and simplify the equation.

\[

$$\begin{align*} 151x+153-153x&=151.97\\ 153 - 2x&=151.97\\ - 2x&=151.97 - 153\\ -2x&=-1.03 \end{align*}$$

\]

Step3: Solve for $x$.

$x=\frac{-1.03}{-2}=0.515$

The abundance of Eu - 151 is $x = 51.5\%$ and the abundance of Eu - 153 is $1 - 0.515=0.485 = 48.5\%$

Answer:

Eu - 151: 51.5%, Eu - 153: 48.5%