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Chapter 2: Problem 49

A mass spectrum of germanium displayed peaks at mass numbers \(70,72,73,74,\) and \(76,\) with relative heights of \(20.5,27.4,7.8,36.5,\) and \(7.8,\) respectively. (a) In the manner of Figure \(2-14,\) sketch this mass spectrum. (b) Estimate the weighted-average atomic mass of germanium, and state why this result is only approximately correct.

Short Answer

Expert verified
The weighted-average atomic mass of germanium is approximately 73.6 atomic mass units.

Step by step solution

01

Sketching the Mass Spectrum

Draw the axis of the graph. The x-axis represents the mass numbers and the y-axis represents the relative abundances. Plot the given points \((70,20.5), (72,27.4), (73,7.8), (74,36.5)\), and \((76,7.8)\). Connect the points with vertical lines from the x-axis.
02

Calculating the Weighted Average

Calculate the relative percentage for each mass number by dividing the relative height by the sum of all relative heights. Multiply each relative percentage by its corresponding mass number. This gives: \((20.5/100)*70+(27.4/100)*72+(7.8/100)*73+(36.5/100)*74+(7.8/100)*76.\)
03

Sum to find the Weighted Average

Add up the products to obtain the estimated weighted-average atomic mass of germanium.

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