To raise the temperature of a certain mass of gas by 50^oC at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100^oC at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

If a semiconductor photodiode can detect a photon with a maximum wavelength of 400 nm, then its band gap energy is :

Planck’s constant h = 6.63 $$ \times $$ 10^–34 J.s. Speed of light c = 3 $$ \times $$ 10⁸ m/s

The radius R of a nucleus of mass number A can be estimated by the formula
R = (1.3 $$ \times $$ 10^–15)A^1/3 m.
It follows that the mass density of a nucleus is of the order of :

(M_prot. $$ \cong $$ M_neut $$ \simeq $$ 1.67 $$ \times $$ 10^–27 kg)

A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take g = 10 m/s² . Assume there is no rotational motion and loss of energy after the collision is negligable.]