The maximum wavelength of incident radiation required to ionize a hydrogen atom in its ground state is nearly

Energy of an electron in $n^{th}$ orbit of hydrogen atom is $\left( {k = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$

Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths $\lambda_1, \lambda_2$ and $\lambda_3$. Given that the wavelengths are in increasing order of magnitude,which one of the following equations correctly relates $\lambda_1, \lambda_2$ and $\lambda_3$?

An electron is in an excited state in a hydrogen-like atom. It has a total energy of $-3.4 \, eV$. If the kinetic energy of the electron is $E$ and its de-Broglie wavelength is $\lambda$,then:

The ratio of the kinetic energies of the electrons in the third and fourth excited states of the hydrogen atom is

The ratio of energies of photons produced due to the transition of an electron in a hydrogen atom from its $(i)$ $3^{\text{rd}}$ to $2^{\text{nd}}$ energy level and (ii) highest energy level to $3^{\text{rd}}$ level is: