A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10 s is ____________ $$\pi$$ $$\times$$ 10^$$-$$1 Nm.

In a semiconductor, the number density of intrinsic charge carries at 27$$^\circ$$C is 1.5 $$\times$$ 10¹⁶/m³. If the semiconductor is doped with impurity atom, the hole density increases to 4.5 $$\times$$ 10²²/m³. The electron density in the doped semiconductor is ___________ $$\times$$ 10⁹/m³.

The nuclear activity of a radioactive element becomes $${\left( {{1 \over 8}} \right)^{th}}$$ of its initial value in 30 years. The half-life of radioactive element is _____________ years.