Question

1. the mass spectrum of a sample of a pure element is given below. calculate the average atomic mass of the element. what is the identity of the element?

Explanation:

Step1: Identify isotopes and abundances

From the mass spectrum, we have isotopes:

• Isotope 1: Mass \( m_1 = 24 \) amu, Abundance \( a_1 = 78.99\% = 0.7899 \)
• Isotope 2: Mass \( m_2 = 25 \) amu, Abundance \( a_2 = 10.00\% = 0.1000 \)
• Isotope 3: Mass \( m_3 = 26 \) amu, Abundance \( a_3 = 11.01\% = 0.1101 \) (since \( 100 - 78.99 - 10.00 = 11.01 \))

Step2: Calculate average atomic mass

The formula for average atomic mass (\( A \)) is:
\[ A = m_1a_1 + m_2a_2 + m_3a_3 \]

Substitute the values:
\[ A = (24 \times 0.7899) + (25 \times 0.1000) + (26 \times 0.1101) \]
\[ A = 18.9576 + 2.5 + 2.8626 \]
\[ A = 24.3202 \approx 24.32 \]

Step3: Identify the element

The average atomic mass of ~24.32 amu corresponds to Magnesium (Mg), as the atomic mass of Mg is approximately 24.31 amu (matching our calculation).

Answer:

The average atomic mass is approximately \( 24.32 \) amu, and the element is Magnesium (Mg).