A particle is confined to the x-axis between x = 0 and x = 1 nm. The potential energy U = 0 inside this region and U is infinite outside. What is the longest possible de Broglie wavelength for the particle?

A. infinite

B. 1 nm

C. 2 nm

D. zero

E. 0.5 nm

According to heisenberg uncertainty Principle

Δx Δp ≥ h / 4π, where Δx is uncertainty in position, Δp is uncertainty in momentum.

Given

Δx = 1 nm

Δp ≥ h / 1nm x 4π

≥ 6.6 x 10⁻³⁴ / 10⁻⁹ x 4 π

≥. 5254 x ⁻²⁵

h / λ ≥. 5254 x ⁻²⁵

6.6 x 10⁻³⁴ /. 5254 x ⁻²⁵ ≥ λ

12.56 x 10⁻⁹ ≥ λ

longest wave length = 12.56 n m