Chapter 7, Problem 10STP

Interpretation Introduction

Interpretation:

The average atomic mass of lutetium needs to be determined.

Concept introduction:

Lutetium is the last element in the lanthanides series. The atomic number of the element is 71. It has two isotopes. Isotopes are those elements which have equal number of proton that means atomic number but different neutrons number. Due to the unequal neutron numbers, the isotopes of elements have different mass.

Answer to Problem 10STP

Atomic mass of lutetium is $175.03\text{ a}\text{.m}\text{.u}$.

Explanation of Solution

Lutetium has two naturally occurring isotope. One is $\text{L}\text{u}$ has an abundance of $97.41\%$ and other isotope $\text{L}\text{u}$ has an abundance of $2.59\%$. To calculate the average atomic mass, calculate the weighted average of the two isotopes.

$\begin{array}{c}\text{Average of the two isotopes=}\left(97.41\%\right)\left(\text{mass}\text{number}\right)\text{+}\left(2.59\%\right)\left(\text{mass}\text{number}\right)\\ =\frac{97.41}{100}\left(175\right)+\frac{2.59}{100}\left(176\right)\\ =\left(0.9741\right)\left(175\right)+\left(0.0259\right)\left(176\right)\\ =170.47+4.56\end{array}$

$\text{Average of the two isotopes}=175\text{.03}\text{a}\text{.m}\text{.u}$

Conclusion

Atomic mass of lutetium is $175.03\text{a}\text{.m}\text{.u}$.