Answered

4. The discovery of isotopes explained why some relative atomic masses are not whole numbers.

Element [tex]$R$[/tex] has two isotopes. Table 1 shows the mass numbers and percentage abundances of the isotopes of element [tex]$R$[/tex].

Table 1

\begin{tabular}{|c|c|}
\hline
Mass number & Percentage abundance [tex]$(\%)$[/tex] \\
\hline
6 & 7.6 \\
\hline
7 & 92.4 \\
\hline
\end{tabular}

Calculate the relative atomic mass ([tex]$A$[/tex]) of element [tex]$R$[/tex]. Give your answer to 1 decimal place. [3 marks]

Relative atomic mass (1 decimal place) [tex]$=$[/tex] ______________



Answer :

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]