Bohr Model of the Hydrogen Atom

The energy of the electron, the hydrogen atom, is known to be expressible in the form

$E_n=\frac{-13.6\text{ eV}}{n^2}\left(n=1,2,3,\mathrm{..........}\right)$

Use this expression, which of the following statement is/are true?

(i) Electron in the hydrogen atom cannot have energy of $–2 \mathrm{eV}$.

(ii) Spacing between the lines (consecutive energy levels) within the given set of the observed hydrogen spectrum decreases as n increases.

The ground state energy of the hydrogen atom is $–13.6 \mathrm{eV}$ . The kinetic and potential energies of electrons in this state are:

Find the ratio of energies of photons produced due to the transition of an electron of a hydrogen atom from its
(i) second permitted energy level to the first level, and
(ii) the highest permitted energy level to the first permitted level.

For a hydrogen atom the value of ionization energy is equal to:

The ground state energy of the hydrogen atom is $–13.6 \mathrm{eV}$. If the electron jumps to the ground state from the third excited state, the wavelength of the emitted photon is

The ground state energy of hydrogen atom is -13.6 eV.

(i) What is the kinetic energy of an electron in the 2nd excited state?

(ii) If the electron jumps to the ground state from the 2nd excited state, calculate the wavelength of the spectral line emitted.

The recoil speed of a hydrogen atom after it emits a photon in going from $n=5$ state to $n=1$ state is

The orbiting speed $v_n$ of $e^{-}$ in the $n^{\mathrm{th}}$ orbit in the case of Positronium is $x-$ fold compared to that in $n^{\mathrm{th}}$ orbit in a hydrogen atom, where $x$ has the value

$1^{\mathrm{st}}$ excitation Potential of a hypothetical hydrogen like sample is $15$ volt. If all the atoms of the sample are in $2^{\text{nd }}$ excited state then find the K.E. in $\mathrm{eV}$ of the electron ejected if a photon of energy $\frac{65}{9}\mathrm{eV}$ is supplied to this sample.

The ratio of magnetic field produced by an electron revolving in first orbit of ${\mathrm{He}}^{+}$ atom to that of the $1^{\mathrm{st}}$ orbit of ${\mathrm{Li}}^{++}$ atom is 

An electron is moving in $n^{th}$ orbit in a Hydrogen like atom with an atomic number $z$. To what the magnetic field at the centre of the nucleus is proportional to?

Orbit velocity of hydrogen atom$\left(\mathrm{v}\right)$ varies with number of orbit $\left(\mathrm{n}\right)$ as

Fine structure constant$\left(\mathrm{\alpha }\right)$ has value

What is the number of spectral lines emitted when the electron of a hydrogen atom moves from $\mathrm{n} = 4$ to $\mathrm{n} = 1$ state?