Which of the following equations describe(s) particle-like behaviour? Which equation describe(s) wave-like behaviour? Do any equations involve both types of behaviour?

$\left(\mathrm{a}\right) \mathrm{C}=\mathrm{\nu \lambda }$

$\left(\mathrm{b}\right) \mathrm{E}={\mathrm{mc}}^2$

$\left(\mathrm{c}\right) \mathrm{r}=\frac{{\mathrm{n}}^2{\mathrm{a}}_0}{\mathrm{Z}}$

$\left(\mathrm{d}\right) \mathrm{E}=\mathrm{h\nu }$

$\left(\mathrm{e}\right) \mathrm{\lambda }=\frac{\mathrm{h}}{\mathrm{m\nu }}$

The quantum numbers listed below are for four different electrons in the same atom. Arrange them in the order of increasing energy. Indicate whether any of the two orbitals have the same energy.

$\left(\mathrm{a}\right) \mathrm{n}=4, \mathrm{l}=0, {\mathrm{m}}_{\mathrm{l}}=0$ and $\mathrm{s}=+\frac{1}{2}$

$\left(\mathrm{b}\right) \mathrm{n}=3, \mathrm{l}=2, {\mathrm{m}}_{\mathrm{l}}=+1$ and $\mathrm{s}=+\frac{1}{2}$

$\left(\mathrm{c}\right) \mathrm{n}=3, \mathrm{l}=2, {\mathrm{m}}_{\mathrm{l}}=-2$ and $\mathrm{s}=-\frac{1}{2}$

$\left(\mathrm{d}\right) \mathrm{n}=3, \mathrm{l}=1, {\mathrm{m}}_{\mathrm{l}}=+1$ and $\mathrm{s}=-\frac{1}{2}$

What is the energy evolved in $\mathrm{J}$ when $1$ mole of $\mathrm{He}-4$ nuclei is produced from protons and neutrons? If $4.9\times {10}^{\mathrm{x}}$ liters of ${\mathrm{C}}_2{\mathrm{H}}_6\left(\mathrm{g}\right)$ are needed at $25°\mathrm{C}$ and $725 \mathrm{mm}$ $\mathrm{Hg}$ to evolve the same quantity of energy when ${\mathrm{C}}_2{\mathrm{H}}_6$ is burnt in ${\mathrm{O}}_2$? Find the value of x.

(Mass of Neutron $=1.008867 \mathrm{amu}$, Mass of proton $=1.00728 \mathrm{amu}$, Mass of $\mathrm{He}=4.0015 \mathrm{amu}$ and $∆{\mathrm{H}}_{\mathrm{comb}}\left({\mathrm{C}}_2{\mathrm{H}}_6\right)=-1427.81 \mathrm{kJ}/\mathrm{mol}$)

Predict the type of radioactive decay process that is likely for each of the following nuclides.

(a) ${}_{92}{}^{228}\mathrm{U}$  (b) ${}_5{}^8\mathrm{B}$  (c) ${}_{29}{}^{68}\mathrm{Cu}$