Particle A has mass m and charge magnitude e, while particle B has mass 9m and charge magnitude 4e. Both particles start from rest and are accelerated through the same potential difference. If λ(A) ÷ λ(B) = N, find N.
Physics · Photoelectric effect and dual nature of matter · debroglie duel nature of light
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Question

Particle A has mass m and charge magnitude e, while particle B has mass 9m and charge magnitude 4e. Both particles start from rest and are accelerated through the same potential difference. If λ(A) ÷ λ(B) = N, find N.

Physics · Photoelectric effect and dual nature of matter · debroglie duel nature of light

G1 Physics · Accepted Answer

For acceleration from rest through the same potential V, λ = h ÷ √(2mqV). Therefore, λ(A) ÷ λ(B) = √[m(B)q(B) ÷ m(A)q(A)]. Substitute: = √[(9m)(4e) ÷ (m)(e)] = √36 = 6. Hence N = 6.