When an electron is accelerated through a potential '$$V$$', the de-Broglie wavelength associated with it is '$$4 \lambda$$'. When the accelerating potential is increased to $$4 \mathrm{~V}$$, its wavelength will be

Compare the rate of loss of heat from a metal sphere at $$627^{\circ} \mathrm{C}$$ with the rate of loss of heat from the same sphere at $$327^{\circ} \mathrm{C}$$, if the temperature of the surrounding is $$27^{\circ} \mathrm{C}$$. (nearly)

In Balmer series, wavelength of the $$2^{\text {nd }}$$ line is '$$\lambda_1$$' and for Paschen series, wavelength of the $$1^{\text {st }}$$ line is '$$\lambda_2$$', then the ratio '$$\lambda_1$$' to '$$\lambda_2$$' is

A coil of '$$n$$' turns and radius '$$R$$' carries a current '$$I$$'. It is unwound and rewound again to make another coil of radius $$\left(\frac{\mathrm{R}}{3}\right)$$, current remaining the same. The ratio of magnetic moment of the new coil to that of original coil is