Rhenium has an atomic number of 75 - AQA - A-Level Chemistry - Question 2 - 2022 - Paper 1

To calculate the relative isotopic mass ($M$) of the unknown isotope, we use the formula:

$M = \frac{(Relative\ Atomic\ Mass) - (Weighted\ Average)}{Relative\ Abundance}$ Substituting the known values:

$M = \frac{(186.3 - (185 \times 10) / (10 + 17))}{17}$

This yields: $M = \frac{(186.3 - 185 \cdot 10 / 27)}{17}$ $M \approx 187.5$

The isotopes of rhenium have the same chemical properties because they have the same number of electrons and therefore the same electronic configuration. Chemical properties are primarily determined by electron configuration.

First, we need to find the mass ($m$) of the $^{186}Re^{+}$ ion:

$m = \frac{185}{6.022 \times 10^{23}} \times 10^{-3} \text{ kg}$

Then we calculate the speed using the kinetic energy formula:

$KE = \frac{1}{2} m v^{2}$ Rearranging for $v$ gives:

$v = \sqrt{\frac{2 \times KE}{m}}$

Substituting in the known values:

$v = \sqrt{\frac{2 \times 1.153 \times 10^{-13}}{m}}$

Finally, we calculate the time ($t$) using:

$t = \frac{d}{v}$ Where $d$ is the distance traveled (1.450 m). Therefore,

$t \approx \frac{1.450}{v}$

The relative abundance of $^{186}Re$ is determined in a TOF mass spectrometer by measuring the intensity of the ion signal corresponding to $^{186}Re$ relative to the total ion current. The signal intensity is proportional to the number of ions detected.