The Bohr orbit radius for the hydrogen atom $(n = 1)$ is approximately $0.530 \ \mathring{A}$. The radius for the first excited state $(n = 2)$ is ............. $\mathring{A}$.

Product $(A)$ is

The area of the region bounded by the curve $y=x^{2}$ and the line $y=16$ is

The conjugate acid of $NH_2^-$ is

$A$ vessel contains a mixture of one mole of oxygen and two moles of nitrogen at $300 \ K$. The ratio of the average rotational kinetic energy per $O_2$ molecule to that per $N_2$ molecule is

In planetary motion,the areal velocity of the position vector of a planet depends on the angular velocity $\omega$ and the distance of the planet from the sun $r$. The correct relation for areal velocity is: