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 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 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

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

According to the rutherford's model, entire positive charge is concentrated in the centre of the atom.

In Bohr's model of hydrogen atom, linear momentum ($p_n$) of the electron depends on the principal quantum number ($n$) as:

Suppose the potential energy between the electron and proton at a distance $r$ is given by $-\frac{k{e}^2}{3r^3}$. Application of Bohr's theory of hydrogen atom, in this case, shows that energy in the $n^{\mathrm{th}}$ orbit is proportional to :

Bohr's theory can be applied to ${\mathrm{Li}}^{+}$ ion.

A photon falls through a height of $1 \mathrm{km}$ through the earth's gravitational field. To calculate the change in its frequency, take its mass to be $\frac{hv}{c^2}$. The fractional change in frequency $v$ is close to