Calculate the atomic mass of element "X" if it has two naturally occurring isotopes with the following masses and natural abundances: Х-45 44.8776 u 32.88% X-47 46.9443 u 67.12% O 46.26 u O 46.84 u O 44.99 u
Calculate the atomic mass of element "X" if it has two naturally occurring isotopes with the following masses and natural abundances: Х-45 44.8776 u 32.88% X-47 46.9443 u 67.12% O 46.26 u O 46.84 u O 44.99 u
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![### Calculation of Atomic Mass
To determine the atomic mass of element "X" which has two naturally occurring isotopes, use the following isotopic masses and their respective natural abundances:
#### Isotope data:
- **Isotope X-45**
- Mass: 44.8776 u
- Natural Abundance: 32.88%
- **Isotope X-47**
- Mass: 46.9443 u
- Natural Abundance: 67.12%
To find the atomic mass of the element, apply the following formula:
#### Formula:
\[
\text{Atomic Mass} = \left( \frac{\text{Mass of Isotope 1} \times \text{Abundance of Isotope 1}}{100} \right) + \left( \frac{\text{Mass of Isotope 2} \times \text{Abundance of Isotope 2}}{100} \right)
\]
#### Calculation:
1. Convert the percentages to decimals:
- Abundance of X-45: \( 32.88\% \) is \( 0.3288 \)
- Abundance of X-47: \( 67.12\% \) is \( 0.6712 \)
2. Apply the formula:
\[
\text{Atomic Mass} = (44.8776 \, \text{u} \times 0.3288) + (46.9443 \, \text{u} \times 0.6712)
\]
3. Calculate:
\[
= (14.75409248 \, \text{u}) + (31.52346016 \, \text{u})
\]
4. Add the results:
\[
= 46.27755264 \, \text{u}
\]
Therefore, the atomic mass of element "X" is approximately **46.28 u**.
#### Multiple Choice Options:
- \( \bigcirc \) **46.26 u**
- ○ 46.84 u
- ○ 44.99 u
- ○ 46.34 u
- ○ 45.91 u
The correct answer is **46.26 u**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bbf8297-dba5-4b47-a922-55444acdea37%2Fce391fc6-623b-451c-8aa1-2b0abdd5fa32%2F2wyxo1s_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculation of Atomic Mass
To determine the atomic mass of element "X" which has two naturally occurring isotopes, use the following isotopic masses and their respective natural abundances:
#### Isotope data:
- **Isotope X-45**
- Mass: 44.8776 u
- Natural Abundance: 32.88%
- **Isotope X-47**
- Mass: 46.9443 u
- Natural Abundance: 67.12%
To find the atomic mass of the element, apply the following formula:
#### Formula:
\[
\text{Atomic Mass} = \left( \frac{\text{Mass of Isotope 1} \times \text{Abundance of Isotope 1}}{100} \right) + \left( \frac{\text{Mass of Isotope 2} \times \text{Abundance of Isotope 2}}{100} \right)
\]
#### Calculation:
1. Convert the percentages to decimals:
- Abundance of X-45: \( 32.88\% \) is \( 0.3288 \)
- Abundance of X-47: \( 67.12\% \) is \( 0.6712 \)
2. Apply the formula:
\[
\text{Atomic Mass} = (44.8776 \, \text{u} \times 0.3288) + (46.9443 \, \text{u} \times 0.6712)
\]
3. Calculate:
\[
= (14.75409248 \, \text{u}) + (31.52346016 \, \text{u})
\]
4. Add the results:
\[
= 46.27755264 \, \text{u}
\]
Therefore, the atomic mass of element "X" is approximately **46.28 u**.
#### Multiple Choice Options:
- \( \bigcirc \) **46.26 u**
- ○ 46.84 u
- ○ 44.99 u
- ○ 46.34 u
- ○ 45.91 u
The correct answer is **46.26 u**.
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