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Identify the information provided by the position and height of a peak in the mass spectrum of an element.
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The horizontal position (m/z) of a peak gives the mass of a specific isotope in amu, while the height of the peak gives the relative abundance of that isotope in a natural sample of the element.
Explain how a mass spectrum can be used to determine the number of naturally occurring isotopes of an element?
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Each distinct peak in the mass spectrum corresponds to one isotope of the element. Counting the number of peaks reveals the number of naturally occurring isotopes, because each isotope has a unique mass that produces a separate signal on the spectrum.
An element’s mass spectrum shows two peaks: one at m/z = 63 with 69.2% relative abundance and one at m/z = 65 with 30.8% relative abundance. Identify the element and its isotopes.
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The element is copper (Cu). The two isotopes are ⁶³Cu (69.2% abundant) and ⁶⁵Cu (30.8% abundant). Copper is the only element with stable isotopes at masses 63 and 65 in these proportions.
Explain why the average atomic mass of an element is rarely a whole number?
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The average atomic mass is a weighted average of the masses of all naturally occurring isotopes, each present in different proportions. Because the contributions of multiple isotopes at different masses are combined, the result is almost never an integer value.
An element has two isotopes. Isotope X has a mass of 10.01 amu with 19.9% abundance, and isotope Y has a mass of 11.01 amu with 80.1% abundance. Calculate the average atomic mass of this element and identify it.
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Equation used: $$\text{Average atomic mass}=({m}_{X}\times {f}_{X})+({m}_{Y}\times {f}_{Y})$$ Given: $${m}_{X}=10.01\text{ amu}, {f}_{X}=0.199$$ $${m}_{Y}=11.01\text{ amu}, {f}_{Y}=0.801$$ Contribution of isotope X: $$10.01\times 0.199=1.992\text{ amu}$$ Contribution of isotope Y: $$11.01\times 0.801=8.819\text{ amu}$$ Sum the contributions: $$1.992+8.819=10.81\text{ amu}$$ The average atomic mass is 10.81 amu, which matches boron (B) on the periodic table.
Predict whether the average atomic mass of an element with two isotopes at masses 85 and 87 would be closer to 85 or 87 if the mass spectrum shows the peak at 85 is approximately three times taller than the peak at 87? Justify your prediction.
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The average atomic mass would be closer to 85 amu. The taller peak at mass 85 indicates that this isotope has a much greater relative abundance (approximately 75%) than the isotope at mass 87 (approximately 25%). In a weighted average, the more abundant isotope pulls the average toward its mass, so the result will be closer to 85 than to 87.
Describe how you would estimate the average atomic mass of an element directly from its mass spectrum without performing a full calculation?
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Identify the mass value of the tallest peak, which represents the most abundant isotope. The average atomic mass will be close to this value but shifted slightly toward the masses of any other peaks present. The larger the secondary peaks relative to the tallest, the more the average is pulled toward their mass values. This provides a quick estimate before performing the weighted-average calculation.