A singly charged positive ion of unknown mass is emitted from rest and accelerated…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A singly charged positive ion of unknown mass m is emitted from rest and accelerated sequentially across two parallel-plate gaps. The first gap has a potential difference of 1.5 kV, and the second gap, located 2.0 cm downstream, has a potential difference of 2.5 kV that acts in the same direction. After leaving the second gap, the ion enters a field-free region 0.50 m long and is detected at the far end. The measured time between the ion’s departure from the second gap and its arrival at the detector is 8.0μs. Non-electric forces are negligible.
(a) Derive an expression for the ion’s speed v1 immediately after crossing the first gap in terms of its charge q, mass m, and the first potential difference.
(b) Determine the ion’s speed v2 immediately after crossing the second gap, expressed in terms of q, m, and the given potential differences.
(c) Using the measured time-of-flight data and your result from part (b), obtain a numerical value for the ratio q/m of the ion.
(d) Suppose the second potential difference were doubled while all other conditions remained the same. Predict qualitatively and quantitatively (no derivation required) how the detector arrival time would change, and justify your reasoning.