The difference between the $n^{\text{th}}$ and $(n+1)^{\text{th}}$ Bohr's radius of a hydrogen atom is equal to the $(n-1)^{\text{th}}$ Bohr's radius. The value of $n$ is:

Phytochrome is a

Work done to increase the temperature of one mole of an ideal gas by $30^{\circ} C$,if it is expanding under the condition $V \propto T^{2/3}$ is,$(R = 8.314 \ J/mol \cdot K)$ (in $J$)

The position vectors of $P$ and $Q$ are respectively $\overrightarrow{a}$ and $\overrightarrow{b}$. If $R$ is a point such that $\overrightarrow{PR}=5 \overrightarrow{PQ}$, then the position vector of $R$ is

$A$ plate of thickness $t$ made of a material of refractive index $\mu$ is placed in front of one of the slits in a double-slit experiment. What should be the minimum thickness $t$ for which the intensity at the centre of the fringe pattern is zero?

$A$ ball is projected from the ground with a velocity $V$ at an angle $\theta$ to the vertical. On its path,it makes an elastic collision with a vertical wall and returns to the ground. The total time of flight of the ball is: