For a non-relativistic particle of fixed mass, consider only very small changes in the relevant quantities. Which relations are correct to first order?
Select all that apply

Question

For a non-relativistic particle of fixed mass, consider only very small changes in the relevant quantities. Which relations are correct to first order?

G1 Physics · Accepted Answer

Since λ = h ÷ p, a small fractional change gives Δλ ÷ λ ≈ −Δp ÷ p. So A is correct. For non-relativistic motion, p = √(2mK), so Δp ÷ p ≈ (1 ÷ 2)(ΔK ÷ K). Therefore, Δλ ÷ λ ≈ −(1 ÷ 2)(ΔK ÷ K). So B is correct. For acceleration from rest, K = qV. Thus ΔK ÷ K = ΔV ÷ V. Therefore, Δλ ÷ λ ≈ −(1 ÷ 2)(ΔV ÷ V). So C is correct. D has the wrong sign and magnitude. Correct answers: A, B and C.