The wavelength of light for the least energetic photons emitted in the Lyman series of the hydrogen spectrum is nearly [Take $$\mathrm{hc}=1240 ~\mathrm{eV}$$ - $$\mathrm{nm}$$, change in energy of the levels $$=10.2 ~\mathrm{eV}$$ ]

In Young's double slit experiment, the wavelength of light used is '$$\lambda$$'. The intensity at a point is '$$\mathrm{I}$$' where path difference is $$\left(\frac{\lambda}{4}\right)$$. If $$I_0$$ denotes the maximum intensity, then the ratio $$\left(\frac{\mathrm{I}}{\mathrm{I}_0}\right)$$ is

$$\left(\sin \frac{\pi}{4}=\cos \frac{\pi}{4}=\frac{1}{\sqrt{2}}\right)$$

The side of a copper cube is $$1 \mathrm{~m}$$ at $$0^{\circ} \mathrm{C}$$. What will be the change in its volume, when it is heated to $$100^{\circ} \mathrm{C}$$ ? $$\left[\alpha_{\text {copper }}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right]$$

If current '$$I$$' is flowing in the closed circuit with collective resistance '$$R$$', the rate of production of heat energy in the loop as we pull it along with a constant speed '$$\mathrm{V}$$' is ( $$\mathrm{L}=$$ length of conductor, $$\mathrm{B}=$$ magnetic field)