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

Let the relative isotopic mass be denoted as x. We can set up the equation based on relative abundance and mass:

[(186.3) = \frac{(185 \times 10) + (x \times 17)}{27} ]

Rearranging gives:

[x = \frac{(186.3 \times 27) - (185 \times 10)}{17}]

Calculating: [x = \frac{(5020.1 - 1850)}{17} = \frac{3170.1}{17} = 186.2]

Thus, the relative isotopic mass of the other rhenium isotope is approximately 186.2.

The isotopes of rhenium have the same chemical properties because they have the same number of electrons and the same electron configuration, which determines their chemical behavior.

Firstly, calculate the mass of the ion using:

[m = \frac{185}{6.022 \times 10^{23}} = 3.072 \times 10^{-25} \text{ kg}]

Using the kinetic energy formula: [KE = \frac{1}{2} mv^2] We rearrange it to find speed (v):

[v = \sqrt{\frac{2 \times KE}{m}} = \sqrt{\frac{2 \times 1.153 \times 10^{-13}}{3.072 \times 10^{-25}}}]

Calculating speed gives: [v = 8.66 \times 10^{5} \text{ ms}^{-1}]

The time (t) taken to travel the distance (d) (1.450 m) is given by:

[t = \frac{d}{v} = \frac{1.450}{8.66 \times 10^{5}} = 1.67 \times 10^{-6} \text{ s}]

The relative abundance of isotopes in a TOF mass spectrometer is determined by measuring the ion detection signal intensity, which corresponds to the number of ions detected. This signal is proportional to the number of isotopes present in the sample.