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Chapter 2: Problem 46

Bromine has two naturally occurring isotopes. One of them, bromine-79, has a mass of 78.918336 u and a natural abundance of \(50.69 \% .\) What must be the mass and percent natural abundance of the other isotope, bromine-81?

Short Answer

Expert verified
The natural abundance of Bromine-81 is \(49.31%\), and the mass is approximately 80.916 u.

Step by step solution

01

Understanding the Problem

Bromine has two isotopes, Bromine-79 and Bromine-81. Given are the mass and natural abundance of Bromine-79. The problem is asking for the mass and natural abundance of Bromine-81.
02

Calculate the Natural Abundance of Bromine-81

Since only two isotopes of bromine exist, the sum of their abundances should be equal to 100%. We have the natural abundance of Bromine-79 as \(50.69%\). Therefore, the natural abundance of Bromine-81 would be \(100 - 50.69 = 49.31%\)
03

Determine the mass of Bromine-81

The weight of an element is calculated as the weighted mean of the weights of its isotopes. The weight of Bromine (Br) is given as approximately 79.904 u. So we can create an equation where \(79.904 = 0.5069 * 78.918336 + 0.4931 * x\), where \(x\) signifies the weight of Bromine-81. Solving this equation for \(x\) gives us the weight of Bromine-81.

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Most popular questions from this chapter

From the densities of the lines in the mass spectrum of krypton gas, the following observations were made: \bullet Somewhat more than \(50 \%\) of the atoms were krypton-84. \(\bullet\) The numbers of krypton- 82 and krypton- 83 atoms were essentially equal. \(\bullet\) The number of krypton-86 atoms was 1.50 times as great as the number of krypton- 82 atoms. \(\bullet\) The number of krypton-80 atoms was \(19.6 \%\) of the number of krypton- 82 atoms. \(\bullet\) The number of krypton- 78 atoms was \(3.0 \%\) of the number of krypton- 82 atoms. The masses of the isotopes are \(^{78} \mathrm{Kr}, 77.9204 \mathrm{u} \quad^{80} \mathrm{Kr}, 79.9164 \mathrm{u} \quad^{82} \mathrm{Kr}, 81.9135 \mathrm{u}\) \(^{83} \mathrm{Kr}, 82.9141 \mathrm{u} \quad^{84} \mathrm{Kr}, 83.9115 \mathrm{u} \quad^{86} \mathrm{Kr}, 85.9106 \mathrm{u}\) The weighted-average atomic mass of \(\mathrm{Kr}\) is \(83.80 .\) Use these data to calculate the percent natural abundances of the krypton isotopes.

\begin{tabular}{l} There are four naturally occurring isotopes of \\ \hline \end{tabular} chromium. Their masses and percent natural abundances are \(49.9461 \mathrm{u}, 4.35 \% ; 51.9405 \mathrm{u}, 83.79 \% ; 52.9407 \mathrm{u}\) \(9.50 \% ;\) and \(53.9389 \mathrm{u}, 2.36 \% .\) Calculate the weightedaverage atomic mass of chromium.

Identify the isotope \(X\) that has one more neutron than protons and a mass number equal to nine times the charge on the ion \(X^{3+}\)

An isotope with mass number 44 has four more neutrons than protons. This is an isotope of what element?

William Prout (1815) proposed that all other atoms are built up of hydrogen atoms, suggesting that all elements should have integral atomic masses based on an atomic mass of one for hydrogen. This hypothesis appeared discredited by the discovery of atomic masses, such as 24.3 u for magnesium and 35.5 u for chlorine. In terms of modern knowledge, explain why Prout's hypothesis is actually quite reasonable.
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