[VISUAL] 1. The mass spectrum of an average sample of a pure element is shown in the figure above. W — Atomic Structure Chemistry Question

STEPS:

1. Understand the concept of mass spectrometry: A mass spectrum is an analytical tool that measures the mass-to-charge ($m/z$) ratio of gaseous ions. For singly charged ions, this directly displays the exact atomic mass (in amu) and the relative percent abundance of each individual isotope present in a sample of an element.
2. Analyze the data from the graph:
- X-axis (Atomic Mass): The peaks are located at 90, 91, 92, 94, and 96 amu.
- Y-axis (Percent Abundance): The heights of the peaks show that the isotope at 90 amu is the most abundant (approx. 51%), followed by 91 amu (approx. 11%), 92 amu (approx. 17%), 94 amu (approx. 17%), and 96 amu (approx. 3%).
3. Estimate the weighted average atomic mass:
- The average atomic mass of an element is the weighted average of its naturally occurring isotopes:
$$\text{Average Mass} = \sum (\text{isotopic mass} \times \text{fractional abundance})$$
$$\text{Average Mass} \approx (90 \times 0.51) + (91 \times 0.11) + (92 \times 0.17) + (94 \times 0.17) + (96 \times 0.03)$$
$$\text{Average Mass} \approx 45.9 + 10.0 + 15.6 + 16.0 + 2.9 = \mathbf{90.4\text{ amu}}$$
- Even without performing exact arithmetic, a student can quickly deduce that because the dominant peak is at 90 amu and all other isotope peaks are heavier, the weighted average must lie slightly above 90 amu (specifically in the 91–92 amu range).
4. Compare the estimated mass with the periodic table values:
- Y (Yttrium): Molar mass $\approx 88.91\text{ amu}$
- Zr (Zirconium): Molar mass $\approx 91.22\text{ amu}$
- Nb (Niobium): Molar mass $\approx 92.91\text{ amu}$
- Th (Thorium): Molar mass $\approx 232.04\text{ amu}$
5. Conclude the correct identity: Zirconium ($\text{Zr}$) is the only element in the list with an average atomic mass matching the mass spectral data ($\approx 91.2\text{ amu}$), confirming Option B is the correct answer.

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WHY_OTHERS_WRONG:

• Option A is incorrect: Yttrium ($\text{Y}$) has an average atomic mass of $88.91\text{ amu}$. If the sample were pure yttrium, the mass spectrum would have its major peak at 89 amu, and there would be no peaks at or above 90 amu.
• Option C is incorrect: Niobium ($\text{Nb}$) has an average atomic mass of $92.91\text{ amu}$. Since niobium is a monoisotopic element, its mass spectrum would feature a single, isolated peak at 93 amu rather than a distribution of five peaks starting at 90 amu.
• Option D is incorrect: Thorium ($\text{Th}$) is a heavy actinide element with an average atomic mass of $232.04\text{ amu}$. This mass is far outside the 86 to 98 amu mass range shown on the x-axis of the spectrum.