Question

the table below gives information about two isotopes of element y.

1. 3**calculate the average atomic mass of element y to the appropriate number of significant figures. show all work.
2. 1**what is the identity of element y?
3. 1**what is the atomic number of element y?
4. 2 write the isotope name and isotopic symbol for isotope 3.

Explanation:

Step1: Calculate the contribution of each isotope

For isotope 1:
The mass is \(m_1 = 19.99\), and the relative abundance \(a_1=90.48\%=0.9048\).
The contribution \(c_1=m_1\times a_1=19.99\times0.9048\)

$$c_1 = 19.99\times0.9048=(20 - 0.01)\times0.9048=20\times0.9048-0.01\times0.9048=18.096 - 0.009048=18.086952$$

For isotope 2:
The mass is \(m_2 = 20.99\), and the relative abundance \(a_2 = 0.27\%=0.0027\)
The contribution \(c_2=m_2\times a_2=20.99\times0.0027=(21 - 0.01)\times0.0027=21\times0.0027-0.01\times0.0027 = 0.0567-0.000027=0.056673\)

For isotope 3:
The mass is \(m_3 = 21.99\), and the relative abundance \(a_3=9.25\% = 0.0925\)
The contribution \(c_3=m_3\times a_3=21.99\times0.0925=(22 - 0.01)\times0.0925=22\times0.0925-0.01\times0.0925=2.035-0.000925 = 2.034075\)

Step2: Sum up the contributions

The average atomic mass \(M=c_1 + c_2 + c_3\)

$$M=18.086952+0.056673 + 2.034075=20.1777\approx20.18$$

• Identity of element \(Y\): The average atomic mass of \(Y\) is approximately \(20.18\). Looking at the periodic table, the element with an atomic mass close to this value is neon (\(Ne\)).
• Atomic number of element \(Y\): Neon has an atomic number of \(10\).
• Isotope name and symbol for isotope 3:
• Isotope name: Neon - 22 (since the mass number is \(21.99\approx22\))
• Isotopic symbol: \(\ce{^{22}_{10}Ne}\)

Answer:

The average atomic mass of element \(Y\) is \(20.18\)