A-LevelPhysicsElectric fields9702/23 · Oct/Nov 2018 · Q57 Marks

A particle of mass m and charge q is in a uniform electric field of strength E. The particle has acceleration a due to the field. The particle has a charge of 4e where e is the elementary charge. The electric field strength is 3.5 × 10⁴ V m⁻¹. The acceleration of the particle is 1.5 × 10¹²ms⁻². A second nucleus that is an isotope of the nucleus in (c) is in the same uniform electric field.

(a)Show that q/m = a/E.[2]
(b)Use the expression in (a) to show that the mass of the particle is 9.0 u.[2]
(c)The particle is a nucleus. State the number of protons and the number of neutrons in the nucleus. number of protons = ..................................................... number of neutrons = .....................................................[1]
(d)(i)State and explain whether the electric field produces, for the two nuclei, the same magnitudes of (i) force,[1]
(d)(ii)(ii) acceleration.[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[M1] E = F/Q
[A1] F = ma and (so) q/m = a/E
[B1] m = (4 × 1.60 × 10⁻¹⁹ × 3.5 × 10⁴)/1.5 × 10¹² (= 1.49 × 10⁻²⁶ kg)
[A1] = 1.49 × 10⁻²⁶/1.66 × 10⁻²⁷ = 9.0 (u)
[A1] protons: 4 and neutrons: 5
[B1] nuclei have the same charge and so same (magnitudes of) force
[B1] nuclei have different masses and same force and so different (magnitudes of) acceleration

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