What is ground state?

In a hydrogen atom,an electron of mass $9.1 \times 10^{-31} \ kg$ revolves about a proton in a circular orbit of radius $0.53 \ \mathring{A}$. The radial acceleration and angular velocity of the electron are respectively:

$A$ hydrogen atom in the ground state absorbs $\Delta E$ amount of energy. If the orbital angular momentum of the electron is increased by $\frac{h}{2 \pi}$ ($h=$ Planck constant), then the magnitude of $\Delta E$ is (in $eV$)

The product of linear momentum and angular momentum of an electron of the hydrogen atom is proportional to $n^{x}$,where $x$ is

$A$ particle of mass $m$ moves in circular orbits with potential energy $V(r) = Fr$,where $F$ is a positive constant and $r$ is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle's orbit is denoted by $R$ and its speed and energy are denoted by $v$ and $E$,respectively,then for the $n^{\text{th}}$ orbit (here $h$ is the Planck's constant)-
$(A)$ $R \propto n^{2/3}$ and $v \propto n^{1/3}$
$(B)$ $R \propto n^{2/3}$ and $v \propto n^{1/3}$
$(C)$ $E = \frac{3}{2} \left( \frac{n^2 h^2 F^2}{4 \pi^2 m} \right)^{1/3}$
$(D)$ $E = 2 \left( \frac{n^2 h^2 F^2}{4 \pi^2 m} \right)^{1/3}$

When a hydrogen atom is in its first excited level,its radius is .... of the Bohr radius.