An electron is revolving in a circular orbit of radius $r$ in a hydrogen atom. The angular momentum of the electron is $L$. The relation between the magnetic dipole moment $(m)$ associated with it,the gyromagnetic ratio $(R)$,and $L$ 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.

In the first excited state of a hydrogen atom, the energy of its electron is $-3.4 \text{ eV}$. The radial distance of the electron from the hydrogen nucleus in this case is approximately: (Take $1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$, $e = 1.6 \times 10^{-19} \text{ C}$ and $\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ N m}^2/\text{C}^2$)

$A$ hydrogen atom in its ground state absorbs $10.2 \; eV$ of energy. The angular momentum of the electron of the hydrogen atom will increase by the value of ............... $\times 10^{-34} \; J \cdot s$ (Given,Planck's constant $h = 6.6 \times 10^{-34} \; J \cdot s$)

Suppose in a hypothetical world, the angular momentum is quantized to be even integral multiples of $\frac{h}{2 \pi}$. According to Bohr's model, what will be the largest possible wavelength emitted by hydrogen atoms in the visible range in this world (in $\text{ nm}$)? (Consider $hc = 1242 \text{ eV-nm}$)

Energy levels $A, B, C$ of a certain atom correspond to increasing values of energy,i.e.,$E_A < E_B < E_C$. If $\lambda_1, \lambda_2, \lambda_3$ are the wavelengths of radiations corresponding to the transitions $C$ to $B$,$B$ to $A$,and $C$ to $A$ respectively,which of the following statements is correct?