Arrange the following :

In the decreasing order of the O - O bond length present in them

O₂, KO₂ and O₂[AsF₄]

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.

A parallelopiped $$'S'$$ has base points $$A, B, C$$ and $$D$$ and upper face points $$A',$$ $$B',$$ $$C'$$ and $$D'.$$ This parallelopiped is compressed by upper face $$A'B'C'D'$$ to form a new parallelopiped $$'T'$$ having upper face points $$A'',B'',C''$$ and $$D''.$$ Volume of parallelopiped $$T$$ is $$90$$ percent of the volume of parallelopiped $$S.$$ Prove that the locus of $$'A''',$$ is a plane.