Question

a sample of a pure element is analyzed using a mass spectrometer to produce the graph provided. estimate the atomic masses and relative abundances of the isotopes shown on the graph, ordered from lowest atomic mass to highest. answers have a 5% tolerance to allow for estimation. what is the average relative atomic mass of the element in the sample? assuming that the sample represents natural abundances found on earth, which element is the sample made up of?

Explanation:

Step1: Identify isotopes and abundances

From the graph, isotope 1: atomic mass \( m_1 = 107 \, u \), relative abundance \( a_1 \approx 50\% = 0.5 \); isotope 2: atomic mass \( m_2 = 109 \, u \), relative abundance \( a_2 \approx 50\% = 0.5 \) (estimating from bar heights).

Step2: Calculate average atomic mass

Use the formula: \( \text{Average Atomic Mass} = m_1 \cdot a_1 + m_2 \cdot a_2 \)
Substitute values: \( (107 \cdot 0.5) + (109 \cdot 0.5) = 53.5 + 54.5 = 108 \, u \) (close to Ag, but let's check the estimation tolerance. Wait, maybe the abundances are ~48% and ~52%? Wait, the first bar (107) is ~50, second (109) ~48? Wait, no, the y-axis for atomic mass: 107, 109. The x-axis (abundance) for 107: up to ~50, 109: up to ~48? Wait, maybe my initial estimate was off. Wait, let's re-express:

Wait, the graph: atomic mass 107 has a bar reaching ~50% (x-axis 0 - 60, so 107: ~50, 109: ~48? Wait, no, the blue bars: first at 107 (atomic mass) with x (abundance) ~50, second at 109 with x ~48? Wait, maybe the correct abundances are \( a_1 \approx 51\% \), \( a_2 \approx 49\% \). Let's recalculate: \( 107 \cdot 0.51 + 109 \cdot 0.49 = 54.57 + 53.41 = 107.98 \approx 108 \, u \). But looking at natural abundances, Silver (Ag) has isotopes 107 (51.839%) and 109 (48.161%), average ~107.87 u. But with 5% tolerance, our estimate of 108 is close.

For the element: The average atomic mass ~108 u, matching Silver (Ag)’s average atomic mass (107.87 u), so the element is Silver (Ag).

Answer:

Average relative atomic mass: \( \boldsymbol{108 \, u} \) (or ~107.9 u with better estimation).
Element: \( \boldsymbol{\text{Silver (Ag)}} \)