In Young's double slit experiment, monochromatic light of wavelength 5000 Å is used. The slits are $1.0 \mathrm{~mm}$ apart and screen is placed at $1.0 \mathrm{~m}$ away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is _________ $\times 10^{-6}$ $\mathrm{m}$.

A coil of 200 turns and area $0.20 \mathrm{~m}^2$ is rotated at half a revolution per second and is placed in uniform magnetic field of $0.01 \mathrm{~T}$ perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is $\frac{2 \pi}{\beta}$ volt. The value of $\beta$ is _______.

A uniform rod $A B$ of mass $2 \mathrm{~kg}$ and length $30 \mathrm{~cm}$ at rest on a smooth horizontal surface. An impulse of force $0.2 \mathrm{~Ns}$ is applied to end B. The time taken by the rod to turn through at right angles will be $\frac{\pi}{x} \mathrm{~s}$, where $x=$ _______ .

A particular hydrogen-like ion emits the radiation of frequency $3 \times 10^{15} \mathrm{~Hz}$ when it makes transition from $n=2$ to $n=1$. The frequency of radiation emitted in transition from $n=3$ to $n=1$ is $\frac{x}{9} \times 10^{15} \mathrm{~Hz}$, when $x=$ ________ .