A sample of iron was ionised by electron impact in a time of flight (TOF) mass spectrometer. Information from the mass spectrum about the isotopes of iron in this sample is shown in Table 1.
Table 1
m/z54565758Abundance / %5.891.72.10.4 \begin{array}{|c|c|c|c|c|} \hline \text{m/z} & 54 & 56 & 57 & 58 \\ \hline \text{Abundance / \%} & 5.8 & 91.7 & 2.1 & 0.4 \\ \hline \end{array} m/zAbundance / %545.85691.7572.1580.4Calculate the relative atomic mass of iron in this sample. Give your answer to one decimal place.
Write an equation, including state symbols, to show how an atom of iron is ionised by electron impact, and give the m/zm/zm/z value of the iron ion that would reach the detector first.
Calculate the mass, in kg, of one atom of 57Fe^{57}\text{Fe}57Fe. The Avogadro constant L=6.022×1023 mol−1L = 6.022 \times 10^{23}\ \text{mol}^{-1}L=6.022×1023 mol−1.
In a TOF mass spectrometer, the time of flight, ttt, of an ion is shown by the equation:
t=dm2E t = d\sqrt{\frac{m}{2E}} t=d2EmIn this equation, ddd is the length of the flight tube, mmm is the mass, in kg, of an ion and EEE is the kinetic energy of the ions. In this spectrometer, the kinetic energy of an ion in the flight tube is 1.360×10−13 J1.360 \times 10^{-13}\ \text{J}1.360×10−13 J. The time of flight of a 54Fe+^{54}\text{Fe}^+54Fe+ ion is 1.112×10−6 s1.112 \times 10^{-6}\ \text{s}1.112×10−6 s. Calculate the time of flight of the 57Fe+^{57}\text{Fe}^+57Fe+ ion. Give your answer to an appropriate number of significant figures.
