For the following reaction

2X(g) $$\to$$ 3Y(g) + 2Z(g)

assuming ideal gas conditions, the data for change of partial pressure with time is as follows:

$$ \begin{array}{llll} \hline \text { Time (in min) } & 0 & 100 & 200 \\ \hline \begin{array}{l} \text { Partial pressure of X } \\ \text { (in mm of Hg) } \end{array} & 800 & 400 & 200 \end{array} $$

Calculate

(A) Order of reaction.

(B) Rate constant.

(C) Time taken for 75% completion of reaction.

(D) Total pressure of the reaction mixture when $$p_x=700$$ mm.

(A) Calculate velocity of electron in the first orbit of hydrogen atom (Given : $$r=a_0=0.529$$ $$\mathop A\limits^o $$).

(B) Calculate the de Broglie's wavelength of the electron in first Bohr orbit.

(C) Calculate the orbital angular momentum of 2p orbital in terms of $$h/2\pi$$ units.

In the following reaction, X is optically active.

$\underset{\mathbf{X}}{\mathrm{C}_5 \mathrm{H}_{13}} \mathrm{~N} \xrightarrow[\mathrm{~N}_2]{\mathrm{NaNO}_2 / \mathrm{HCl}} \mathbf{Y}($ Tertiary alcohol $)+$ Other products

Find X and Y. Is y optically active? Write all the intermediate steps.

Give reasons :