Sodium metal crystallizes in a body-centred cubic $(bcc)$ lattice with a unit cell edge of $4.29 \ \mathring{A}$. The radius of the sodium atom is approximately: .............. $\mathring{A}$

$A$ particle of mass $m$ moves along line $PC$ with velocity $v$ as shown. What is the angular momentum of the particle about $O$?

The Henry's law constant for the solubility of $N_2$ gas in water at $298 \ K$ is $1.0 \times 10^5 \ atm$. The mole fraction of $N_2$ in air is $0.8$. The number of moles of $N_2$ from air dissolved in $10 \ moles$ of water at $298 \ K$ and $5 \ atm$ pressure is

Which one of the following is an artificial sweetening agent?

Two moles of ideal helium gas are in a rubber balloon at $30^\circ C$. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to $35^\circ C$. The amount of heat required in raising the temperature is nearly...... $J$ (take $R = 8.31$ $J/mol \cdot K$)

In order to shift a body of mass $m$ from a circular orbit of radius $3R$ to a higher radius $5R$ around the Earth,the work done is: