The total energy of an electron in the ground state of a hydrogen atom is $-13.6 \text{ eV}$. The kinetic energy of an electron in the first excited state is.....$\text{ eV}$

What is the excited state of an atom?

As the $n$ (number of orbit) increases,the difference of energy between the consecutive energy levels

In a sample of hydrogen-like atoms,all of which are in the ground state,a photon beam containing photons of various energies is passed. In the absorption spectrum,five dark lines are observed. The number of bright lines in the emission spectrum will be (assume that all transitions take place).

$A$ photon of wavelength $\lambda$ is absorbed by an electron confined to a box of length $L = \sqrt{(35 h \lambda / 8 m c)}$. As a result,the electron makes a transition from state $k=1$ to the state $n$. Subsequently,the electron transitions from the state $n$ to the state $m$ by emitting a photon of wavelength $\lambda^{\prime} = 1.75 \lambda$. Then,

In hydrogen and hydrogen-like atoms,the ratio of the difference of energies $E_{4n}-E_{2n}$ and $E_{2n}-E_{n}$ varies with its atomic number $Z$ and $n$ as: