Physics • Year 12 • Module 6 • Lesson 18 • Enrichment
Mass Spectrometers
Lock in the core vocabulary, the radius-of-curvature formula, and the purpose of each spectrometer stage before tackling harder problems.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: mass spectrometer, velocity selector, mass-to-charge ratio (m/q), isotopes, centripetal force, magnetic analyser, ionisation, radius of curvature, atomic mass unit (u), magnetic force. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | An instrument that separates ions by their mass-to-charge ratio using electric and magnetic fields. | |
| 1.2 | A region of crossed electric and magnetic fields through which only ions with the speed v = E/B pass undeflected. | |
| 1.3 | The ratio that determines how much an ion curves in a magnetic field; ions with a smaller value curve more sharply. | |
| 1.4 | Atoms of the same element that have different numbers of neutrons and therefore different masses but the same charge. | |
| 1.5 | The inward force needed to keep an object moving in a circular path: F = mv²/r. | |
| 1.6 | The region of uniform magnetic field in a spectrometer where ions travel in circular arcs whose radius reveals m/q. | |
| 1.7 | The process of removing electrons from neutral atoms so they carry a net electric charge and can be deflected by fields. | |
| 1.8 | The distance from the centre of a circular path to the ion; given by r = mv/(qB) for a charged particle in a uniform magnetic field. | |
| 1.9 | A unit of mass approximately equal to 1.661 × 10−27 kg; approximately the mass of a proton or neutron. | |
| 1.10 | The force exerted on a moving charged particle by a magnetic field; its direction is perpendicular to both the velocity and the field. |
2. True or false — with correction
Circle T or F. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 In a mass spectrometer, the magnetic force acts as the centripetal force that keeps an ion moving in a circular arc. T / F
2.2 A heavier ion (larger mass) travelling at the same speed and charge as a lighter ion will curve more sharply in a uniform magnetic field. T / F
2.3 In a velocity selector, the speed of ions that pass through undeflected depends on both the ion’s mass and charge. T / F
2.4 If the magnetic field strength B in the analyser is doubled while all other quantities remain the same, the radius of curvature of the ion’s path is halved. T / F
2.5 Isotopes of the same element carry the same charge when singly ionised, so they can be separated by a mass spectrometer because they travel at different speeds. T / F
2.6 The four stages of a mass spectrometer in order are: ionisation, acceleration, velocity selection, and magnetic analysis. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word or phrase is used once. 8 marks (1 per blank)
Word bank:
centripetal · circular · E/B · heavier · lighter · mass-to-charge ratio · mv/(qB) · perpendicular
When a charged particle moves through a magnetic field, the magnetic force acts ___________ to its velocity, causing it to follow a ___________ path. This magnetic force provides the ___________ force required for circular motion. The radius of curvature is given by r = ___________. Ions with a smaller ___________ curve more sharply. Therefore, ___________ ions (smaller mass) produce smaller radii and ___________ ions produce larger radii. A velocity selector ensures all ions enter the analyser at the same speed v = ___________.
4. Formula recall
Answer each question in 1–2 sentences using precise terms and symbols. 8 marks (2 each)
4.1 State the formula for the radius of curvature r of a charged particle in a uniform magnetic field and identify all symbols.
4.2 Write the force balance equation that is used to derive r = mv/(qB), showing both forces that are equated.
4.3 State the condition for a velocity selector and explain why the selected speed v = E/B is the same for all ions, regardless of their mass or charge.
4.4 In the magnetic analyser, what quantity is directly measured from the radius of curvature, and why is it necessary that all ions have the same speed when they enter this region?
5. Sequence the stages of a mass spectrometer
The five descriptions below are out of order. Number them 1–5 to show the correct sequence, then write a one-sentence purpose for each stage. 10 marks (1 sequence + 1 purpose each)
| Order (1–5) | Stage description | Purpose (one sentence) |
|---|---|---|
| Ions enter a uniform magnetic field and follow curved circular paths whose radius depends on m/q. | ||
| Neutral atoms have electrons removed by electron bombardment or other methods to produce positively charged ions. | ||
| Ions are accelerated through a potential difference to give them kinetic energy. | ||
| The detector records where different ions land, revealing their mass-to-charge ratio. | ||
| Crossed electric and magnetic fields select only ions with speed v = E/B to pass through undeflected. |
Q1 — Term–definition match
1.1 mass spectrometer • 1.2 velocity selector • 1.3 mass-to-charge ratio (m/q) • 1.4 isotopes • 1.5 centripetal force • 1.6 magnetic analyser • 1.7 ionisation • 1.8 radius of curvature • 1.9 atomic mass unit (u) • 1.10 magnetic force.
Q2 — True / false with correction
2.1 True. The magnetic force F = qvB acts perpendicular to the ion’s velocity, providing the centripetal force mv²/r needed for circular motion.
2.2 False. A heavier ion curves less sharply (has a larger radius). From r = mv/(qB), a larger mass m produces a larger radius r, so the heavier ion follows a wider arc.
2.3 False. The selected speed v = E/B depends only on the electric field E and magnetic field B, not on the ion’s mass or charge. This is because the charge q cancels out in the force balance qE = qvB.
2.4 True. From r = mv/(qB), radius is inversely proportional to B. Doubling B halves r.
2.5 False. Isotopes of the same element carry the same charge when singly ionised AND travel at the same speed (after the velocity selector), so they are separated because they have different masses, which produces different radii of curvature in the magnetic analyser.
2.6 True. Ionisation → acceleration → velocity selection → magnetic analysis is the correct sequence.
Q3 — Cloze paragraph
In order: perpendicular / circular / centripetal / mv/(qB) / mass-to-charge ratio / lighter / heavier / E/B.
Q4.1 — Radius of curvature formula
r = mv/(qB), where r = radius of curvature (m), m = mass of ion (kg), v = speed of ion (m/s), q = charge on ion (C), B = magnetic field strength in the analyser (T).
Q4.2 — Force balance derivation
The magnetic force (F = qvB) is equated to the centripetal force (F = mv²/r): qvB = mv²/r. Dividing both sides by v and rearranging gives r = mv/(qB).
Q4.3 — Velocity selector condition
The condition is qE = qvB, which simplifies to v = E/B. The charge q appears on both sides of the equation and cancels, so the selected speed depends only on the field values E and B, not on m or q. Every ion with speed E/B passes through undeflected regardless of its mass or charge.
Q4.4 — Quantity measured and need for uniform speed
The radius r directly measures the mass-to-charge ratio (m/q) of the ion: rearranging r = mv/(qB) gives m/q = rB/v. If ions had different speeds, a larger r could result from either a heavier mass or a higher speed, making it impossible to determine mass from radius alone. The velocity selector ensures v is identical for all ions, so r depends only on m/q.
Q5 — Stage sequencing
Correct order and purposes:
1 — Ionisation: Neutral atoms have electrons removed to produce charged ions that can be deflected by electric and magnetic fields.
2 — Acceleration: Ions are accelerated through a potential difference to give them kinetic energy and a well-defined speed range.
3 — Velocity selection: Crossed E and B fields select only ions with speed v = E/B so that all ions entering the analyser travel at the same speed.
4 — Magnetic analysis: A uniform magnetic field bends ions into circular paths whose radius reveals their mass-to-charge ratio.
5 — Detection: The detector records where each ion lands; since all ions have the same v and B, position depends only on m/q, allowing masses to be identified.