To calculate the relative atomic mass (A) of element [tex]\( R \)[/tex], we need to use the mass numbers and their respective percentage abundances. The formula to calculate the relative atomic mass is:
[tex]\[ A = \left( m_1 \times \frac{a_1}{100} \right) + \left( m_2 \times \frac{a_2}{100} \right) \][/tex]
where:
- [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] are the mass numbers of the isotopes.
- [tex]\( a_1 \)[/tex] and [tex]\( a_2 \)[/tex] are the percentage abundances of the isotopes.
From the given data in Table 1:
- Mass number of isotope 1 ([tex]\( m_1 \)[/tex]) is 6, with a percentage abundance ([tex]\( a_1 \)[/tex]) of 7.6%.
- Mass number of isotope 2 ([tex]\( m_2 \)[/tex]) is 7, with a percentage abundance ([tex]\( a_2 \)[/tex]) of 92.4%.
Now, let's substitute these values into the formula:
[tex]\[
A = \left( 6 \times \frac{7.6}{100} \right) + \left( 7 \times \frac{92.4}{100} \right)
\][/tex]
First, calculate the individual contributions of each isotope to the relative atomic mass:
[tex]\[
6 \times \frac{7.6}{100} = 6 \times 0.076 = 0.456
\][/tex]
[tex]\[
7 \times \frac{92.4}{100} = 7 \times 0.924 = 6.468
\][/tex]
Next, add these contributions together:
[tex]\[
A = 0.456 + 6.468 = 6.924
\][/tex]
Finally, we round the result to 1 decimal place:
[tex]\[
A \approx 6.9
\][/tex]
Therefore, the relative atomic mass of element [tex]\( R \)[/tex] to 1 decimal place is:
[tex]\[ \boxed{6.9} \][/tex]
