The Tof Spectrometer 5-marker

In almost every A-level and AS-level exam, there is a 5-mark question about an ion being accelerated by a TOF-mass spectrometer. You are either given the mass of the ion and asked to work out how long it takes to reach the detector, or you are given how long it takes a mystery ion to reach the detector, and asked the mass of the ion. Either way, you should be rejoicing when you see this question, because if you know the step-by-step process to answer this question, these will be easy marks. Let`s work through an example of each:

Case 1: How long to reach the detector

(example taken from AQA A-level 2022, paper 2, question 2.4)

"A sample of rhenium is ionised by electron impact in a time of flight (TOF) mass spectrometer.

A ¹⁸⁵Re⁺ ion with a kinetic energy of 1.153 × 10⁻¹³ J travels through a 1.450 m flight tube.

The kinetic energy of the ion is given by the equation KE = (1/2) mv²

where

m = mass / kg

v = speed / m s^–1

KE = kinetic energy / J

Calculate the time, in seconds, for the ion to reach the detector.

The Avogadro constant, L = 6.022 × 10²³ mol⁻¹

Step 1: Find the mass of your ion

We know that one mole of ¹⁸⁵Re⁺ weighs 185g = 0.185kg from the mass number provided. We are being asked about a single ion here, so to find the mass of a single ion, we simply divide the mass of a mole of ions by the Avogadro constant:

Mass = 0.185 ÷ 6.022 × 10²³

Mass = 3.0721 × 10⁻²⁵ kg

Step 2: Plug the numbers into the KE equation and solve for speed

We`ve been given the KE of the ion already, and now we know its mass, we can plug all the numbers in, and solve for speed:

KE = (1/2) mv²

1.153 × 10⁻¹³ = (1/2) × (3.0721 × 10⁻²⁵) × v²

(1.153 × 10⁻¹³ × 2) ÷ (3.0721 × 10⁻²⁵) = v²

v² = 7.5063 × 10¹¹

v = 8.664 × 10⁵ m s^-1

Step 3: Calculate time taken

time = distance ÷ speed

time = 1.45 ÷ 8.664 × 10⁵

time = 1.67 × 10⁻⁶ seconds

Case 2: Work out the mass of the ion

(example taken from AQA A-level 2022, paper 2, question 2.4)

"A molecule Q is ionised by electron impact in a TOF mass spectrometer.

The Q⁺ ion has a kinetic energy of 2.09 × 10^–15 J

This ion takes 1.23 × 10^–5 s to reach the detector.

The length of the flight tube is 1.50 m

Calculate the relative molecular mass of Q.

KE = (1/2) mv² where m = mass (kg) and v = speed (m s^–1 ) The Avogadro constant, L = 6.022 × 10²³ mol^–1

You`ll notice that the steps in case 2 are essentially the reverse of the steps in case 1!

Step 1: Find the speed of the ion

speed = distance / time

speed = 1.50 / (1.23 × 10^–5)

speed = 1.2195 × 10⁵ m s^–1

Step 2: Plug the numbers into the KE equation, and solve for mass

We`ve been given the KE of the Q⁺ ion already, and now we know its speed, so we can plug all the numbers in, and solve for mass:

KE = (1/2) mv²

2.09 × 10^–15 = (1/2) × m × (1.2195 × 10⁵)2

(2.09 × 10^–15 × 2) ÷ (1.2195 × 10⁵)2 = m

m = 2.8107 × 10^-25 kg

Step 3: Convert the mass of a single ion into the relative molecular mass

Remember, the relative molecular mass is the mass of a mole of ions, in grams so to convert our mass of a single ion into a mass of a mole of ions, simply multiply by Avogadro`s number, and then multiply by 1000 to convert to grams.

Relative molecular mass = (2.8107 × 10^-25) × (6.022 × 10²³)

Relative molecular mass = 0.1693kg

Relative molecular mass = 169

Summary

These questions can look daunting at first, but they all follow the same pattern: work out either mass or velocity, plug it into the KE equation, then find the missing value. Keep a close eye on units, and remember that velocity is squared in the KE equation. Other than that, if you follow these steps, you shouldn`t have any issue getting 5/5 on this question every time!