Bohr’s Model of 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.

A hydrogen atom initially in the ground level absorbs a photon which excites it to the $n=4$ level. Determine the wavelength of the photon.

The Bohr orbit radius for the hydrogen atom (n = 1) is approximately  $0.530\AA .$  The radius for the first excited state (n = 2) orbit is  $(in\AA )$

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

Some wavelengths observed in the emission spectrum of neutral hydrogen gas are $912, 1026, 1216, 3646, 6563 \stackrel{\circ }{\mathrm{A}}$. If broad band light is passing through neutral hydrogen gas at room temperature, then the wavelength that will not be absorbed strongly is,

The allowed energy levels of electrons in a Hydrogen atom are given by $E_n=-\frac{13.6}{n^2} \mathrm{eV}$. For electronic transition in Hydrogen atom, what is the maximum frequency of the emitted photon?

$\left(h=6.62\times {10}^{-34} \mathrm{Js}; e=1.6\times {10}^{-19} \mathrm{C}\right)$

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

${\lambda }_2$ and ${\lambda }_4$ are the wavelengths of photons required to excite the Hydrogen atom from its ground state to its second and fourth excited states, respectively. What is the correct ratio ${\lambda }_2/{\lambda }_4$ ?