The half-life of Au¹⁹⁸ is 2.7 days. The activity of 1.50 mg of Au¹⁹⁸ if its atomic weight is 198 g mol^$$-$$1 is, (N_a = 6 $$\times$$ 10²³/mol).

Calculate the value of mean free path ($$\lambda$$) for oxygen molecules at temperature 27$$^\circ$$C and pressure 1.01 $$\times$$ 10⁵ Pa. Assume the molecular diameter 0.3 nm and the gas is ideal. (k = 1.38 $$\times$$ 10^$$-$$23 JK^$$-$$1)

A charge Q is moving $$\overrightarrow {dl} $$ distance in the magnetic field $$\overrightarrow {B} $$. Find the value of work done by $$\overrightarrow {B} $$.

In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1m (measured using a scale of least count = 1 mm), a weight of mass 1 kg (measured using a scale of least count = 1 g) was hanged to get the elongation of 0.5 cm (measured using a scale of least count 0.001 cm). What will be the fractional error in the value of Young's Modulus determined by this experiment?