Agas of helium atoms at 273 k is in a cubical container with 25.0 cm on a side. (a) what is the minimum uncertainty in momentum components of helium atoms? (b) what is the minimum uncertainty in velocity components? (c) find the ratio of the uncertainties in (b) to the mean speed of an atom in each direction.

wave function of a particle with mass m is given by ψ(x)={ Acosαx−

π

2α

≤x≤+

π

2α

0otherwise , where α=1.00×1010/m.

(a) Find the normalization constant.

(b) Find the probability that the particle can be found on the interval 0≤x≤0.5×10−10m.

(c) Find the particle’s average position.

(d) Find its average momentum.

(e) Find its average kinetic energy −0.5×10−10m≤x≤+0.5×10−10m.