If $E$ and $L$ denote the magnitudes of total energy and of angular momentum of an electron in a Bohr orbit,then the true relation between them is:

The electric potential between a proton and an electron is given by $V = V_0 \ln(r/r_0)$,where $r_0$ is a constant. Assuming Bohr's model to be applicable,find the variation of $r_n$ with $n$,where $n$ is the principal quantum number.

The ratio of the total energy of the $2^{\text{nd}}$ orbit electron for the hydrogen atom $(_1H^1)$ to that of the helium ion $(He^+)$ $(_2^4He)$ is:

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 . . . . . . .

Ionization potential of a hydrogen atom is $13.6 \text{ eV}$. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy $12.1 \text{ eV}$. According to Bohr's theory,the number of spectral lines emitted by the hydrogen atoms will be:

If the radius of the first Bohr orbit in a hydrogen atom is $0.53 \, \mathring A$,then the radius of the third Bohr orbit will be ....... $\mathring A$.