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If titanium (Ti) has 3 naturally occurring isotopes, titanium-47 (43.5%), titanium-48 (44.1%), and titanium-50 (12.4%), what is its average atomic mass?

A. 21.168
B. 47.8
C. 2.23
D. 20.445

Sagot :

To determine the average relative atomic mass of titanium, given its three naturally occurring isotopes and their respective abundances, follow these steps:

1. Identify the mass and abundance of each isotope:
- Titanium-47 has a mass of 47 and an abundance of 43.5%.
- Titanium-48 has a mass of 48 and an abundance of 44.1%.
- Titanium-50 has a mass of 50 and an abundance of 12.4%.

2. Convert the percentages into decimal form:
- Titanium-47: 43.5% becomes 0.435.
- Titanium-48: 44.1% becomes 0.441.
- Titanium-50: 12.4% becomes 0.124.

3. Calculate the contribution of each isotope to the average atomic mass:
- Contribution of Titanium-47: [tex]\( 47 \times 0.435 \)[/tex].
- Contribution of Titanium-48: [tex]\( 48 \times 0.441 \)[/tex].
- Contribution of Titanium-50: [tex]\( 50 \times 0.124 \)[/tex].

4. Sum the contributions to find the average atomic mass:
[tex]\[ \text{Average atomic mass} = (47 \times 0.435) + (48 \times 0.441) + (50 \times 0.124) \][/tex]

This simplifies to:
[tex]\[ \text{Average atomic mass} = 20.445 + 21.168 + 6.2 \][/tex]

5. Add the results:
[tex]\[ \text{Average atomic mass} = 47.813 \][/tex]

Therefore, the average relative atomic mass of titanium is approximately 47.813.

Given the answer choices:
A. 21.168
B. 47.8
C. 2.23
D. 20.445

The closest answer to our calculated value is:
B. 47.8.