Question

1. an element has three naturally occurring isotopes. isotope 1 has a mass of 19.992 amu. isotope 2 has a mass of 20.994 amu. isotope 3 has a mass of 21.991 amu. the pie graph shows the relative abundance of each isotope. a. calculate the atomic mass of the element. b. identify the element, using the periodic table.

Explanation:

Step1: Calculate the contribution of each isotope

The formula for atomic mass \(M = m_1\times a_1 + m_2\times a_2 + m_3\times a_3\), where \(m_i\) is the mass of isotope \(i\) and \(a_i\) is the abundance (in decimal form) of isotope \(i\).
For Isotope 1: \(m_1 = 19.992\) amu, \(a_1=0.9051\). Contribution \(=19.992\times0.9051\)

$$19.992\times0.9051=(20 - 0.008)\times0.9051=20\times0.9051-0.008\times0.9051=18.102 - 0.0072408 = 18.0947592$$

For Isotope 2: \(m_2 = 20.994\) amu, \(a_2 = 0.0027\). Contribution \(=20.994\times0.0027=(21-0.006)\times0.0027=21\times0.0027- 0.006\times0.0027=0.0567-0.0000162 = 0.0566838\)
For Isotope 3: \(m_3=21.991\) amu, \(a_3 = 0.0922\). Contribution \(=21.991\times0.0922=(22-0.009)\times0.0922=22\times0.0922-0.009\times0.0922=2.0284 - 0.0008298=2.0275702\)

Step2: Sum up the contributions

\(M=18.0947592 + 0.0566838+2.0275702\)

$$M=(18.0947592+2.0275702)+0.0566838=20.1223294+0.0566838 = 20.1790132\approx20.18$$

Answer:

a. The atomic mass of the element is approximately \(20.18\) amu.
b. Looking at the periodic table, the element with an atomic mass of approximately \(20.18\) amu is Neon (\(Ne\)).