In which of the following systems will the radius of the first orbit $(n = 1)$ be minimum?

An electron in the hydrogen atom initially in the fourth excited state makes a transition to $n^{\text{th}}$ energy state by emitting a photon of energy $2.86 \ eV$. The integer value of $n$ will be . . . . . . .

The de-Broglie wavelength $(\lambda_B)$ associated with the electron orbiting in the second excited state of a hydrogen atom is related to that in the ground state $(\lambda_G)$ by:

For a certain hypothetical one-electron atom,the wavelength (in $\mathring{A}$) for the spectral lines for transition from $n = p$ to $n = 1$ is given by $\lambda = \frac{1500p^2}{p^2 - 1}$ (where $p > 1$). The ionization potential of this element must be .....$V$ (Take $hc = 12420\ eV\cdot\mathring{A}$).

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:

Using the Bohr model,calculate the electric current created by the electron when the $H$-atom is in the ground state.