The electron in a hydrogen atom makes a transition $n_1 \to n_2$,where $n_1$ and $n_2$ are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times that in the final state. The possible values of $n_1$ and $n_2$ are

If the force between the electron in the first Bohr orbit and the nucleus (proton) in a hydrogen atom is $F$,then the force between them when the electron is in the second orbit is

The angular momentum for the electron in the first Bohr orbit is $L$. If the electron is assumed to revolve in the second orbit of a hydrogen atom,then the change in angular momentum will be:

The ionisation energy of a hydrogen atom is $13.6 \; eV$. The ionisation energy of a singly ionised helium atom would be ....... $eV$.

An electron in a hydrogen atom is replaced by an identically charged particle,a muon,with a mass $207$ times that of an electron. What will be the radius of the $K$ shell?

$A$ particle of mass $m$ is moving in a circular orbit under the influence of the central force $F(r) = -kr$,corresponding to the potential energy $V(r) = \frac{1}{2}kr^2$,where $k$ is a positive force constant and $r$ is the radial distance from the origin. According to Bohr's quantization rule,the angular momentum of the particle is given by $L = n\hbar$,where $\hbar = \frac{h}{2\pi}$,$h$ is Planck's constant,and $n$ is a positive integer. If $v$ and $E$ are the speed and total energy of the particle,respectively,then which of the following expression$(s)$ is(are) correct?
$(A)$ $r^2 = n\hbar \sqrt{\frac{1}{mk}}$
$(B)$ $v^2 = n\hbar \sqrt{\frac{k}{m^3}}$
$(C)$ $\frac{L}{mr^2} = \sqrt{\frac{k}{m}}$
$(D)$ $E = \frac{n\hbar}{2} \sqrt{\frac{k}{m}}$