Question

An element has three naturally occurring isotopes with the following masses and abundances.
Isotopic mass 27.977, 28.976, 29.974 and fractional abundance 0.9221, 0.0470 and 0.0309;
Calculate the atomic mass of this element and what is the identify of this element

Answer 1

To calculate the atomic mass of an element with multiple isotopes, you can use the formula:

\[
\text{Atomic Mass} = \sum (\text{Isotopic Mass} \times \text{Fractional Abundance})
\]

Let's break this down for the given isotopes:

1. Isotope 1:
- Isotopic mass = 27.977 amu
- Fractional abundance = 0.9221
- Contribution to atomic mass = \( 27.977 \times 0.9221 \)

2. Isotope 2:
- Isotopic mass = 28.976 amu
- Fractional abundance = 0.0470
- Contribution to atomic mass = \( 28.976 \times 0.0470 \)

3. Isotope 3:
- Isotopic mass = 29.974 amu
- Fractional abundance = 0.0309
- Contribution to atomic mass = \( 29.974 \times 0.0309 \)

Now let’s calculate each contribution:

1. For the first isotope:
\[
27.977 \times 0.9221 = 25.752
\]

2. For the second isotope:
\[
28.976 \times 0.0470 = 1.360
\]

3. For the third isotope:
\[
29.974 \times 0.0309 = 0.926
\]

Now, sum these contributions to find the atomic mass:

\[
\text{Atomic Mass} = 25.752 + 1.360 + 0.926 = 28.038 \, \text{amu}
\]

Thus, the calculated atomic mass of the element is approximately **28.038 amu**.

Now, to identify the element, we can refer to the periodic table. The atomic mass of 28.038 amu closely corresponds to **Silicon (Si)**, which has an atomic mass of approximately 28.085 amu. Silicon has three naturally occurring isotopes: Si-28, Si-29, and Si-30, which are consistent with the isotopes provided in the problem.

So, the element is **Silicon (Si)**.