A 137Ba+^{137}\text{Ba}^+137Ba+ ion is accelerated in a time-of-flight (TOF) mass spectrometer, gaining a kinetic energy of 2.12 × 10-16 J. The ion then enters a field-free drift region (flight tube), taking 3.65 × 10-5 s to traverse its entire length and reach the detector.
KE=12mv2where m=mass (kg) and v=speed (m s−1) \text{KE} = \frac{1}{2}mv^2 \quad \text{where } m = \text{mass (kg) and } v = \text{speed (m s}^{-1}\text{)} KE=21mv2where m=mass (kg) and v=speed (m s−1)The Avogadro constant, L=6.022×1023 mol−1L = 6.022 \times 10^{23}\text{ mol}^{-1}L=6.022×1023 mol−1
Calculate the length of the flight tube in metres. Give your answer to the appropriate number of significant figures.