A ball of mass 100 g is moving with 100 ms^-1. Find it's wavelength.

(a) The Schrodinger wave equation for hydrogen atom is

$$$\psi = {1 \over {4\sqrt {2\pi } }}{\left( {{1 \over {{a_0}}}} \right)^{3/2}}\left( {2 - {{{r_0}} \over {{a_0}}}} \right){e^{ - {r_0}/{a_0}}}$$$
Where a₀ is Bohr's radius. If the radial node in 2s be at r₀, then find r₀ in terms of a₀.

(b) A baseball having mass 100 g moves with velocity 100 m/s. Determine the value of wavelength of baseball.

Find the equation of plane passing through $$(1, 1, 1)$$ & parallel to the lines $${L_1},{L_2}$$ having direction ratios $$(1,0,-1),(1,-1,0).$$ Find the volume of tetrahedron formed by origin and the points where these planes intersect the coordinate axes.

$${P_1}$$ and $${P_2}$$ are planes passing through origin. $${L_1}$$ and $${L_2}$$ are two line on $${P_1}$$ and $${P_2}$$ respectively such that their intersection is origin. Show that there exists points $$A, B, C,$$ whose permutation $$A',B',C'$$ can be chosen such that (i) $$A$$ is on $${L_1},$$ $$B$$ on $${P_1}$$ but not on $${L_1}$$ and $$C$$ not on $${P_1}$$ (ii) $$A'$$ is on $${L_2},$$ $$B'$$ on $${P_2}$$ but not on $${L_2}$$ and $$C'$$ not on $${P_2}$$