Question

select the correct answer.
thallium consists of 29.5%tl-203 and 70.5%tl-205. what is the relative atomic mass of thallium?
a. 203amu
b. 204 amu
c. 203.5 amu
d. 205.3amu
e. 204.4 amu

Explanation:

Step1: Recall the formula for relative atomic mass

The relative atomic mass ($A_r$) of an element with isotopes is calculated by the weighted average of the masses of its isotopes, where the weights are the relative abundances (in decimal form) of the isotopes. The formula is:
$$A_r = (m_1 \times f_1) + (m_2 \times f_2) + \dots + (m_n \times f_n)$$
where $m_i$ is the mass of isotope $i$, and $f_i$ is the fractional abundance of isotope $i$.

Step2: Convert percentages to fractions

For Tl - 203: Abundance = 29.5% = $\frac{29.5}{100}$ = 0.295
For Tl - 205: Abundance = 70.5% = $\frac{70.5}{100}$ = 0.705

Step3: Calculate the contribution of each isotope

• Contribution of Tl - 203: $203 \times 0.295$

$203 \times 0.295 = 203 \times (0.3 - 0.005) = 203 \times 0.3 - 203 \times 0.005 = 60.9 - 1.015 = 59.885$

• Contribution of Tl - 205: $205 \times 0.705$

$205 \times 0.705 = 205 \times (0.7 + 0.005) = 205 \times 0.7 + 205 \times 0.005 = 143.5 + 1.025 = 144.525$

Step4: Sum the contributions

Add the two contributions to get the relative atomic mass:
$A_r = 59.885 + 144.525 = 204.41$ (approx 204.4 amu)

Answer:

E. 204.4 amu