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.

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

An electron in a hydrogen atom in its ground state absorbs energy equal to the ionisation energy of ${\mathrm{Li}}^{+2}$ . Calculate the wavelength of the emitted electron.

If an object contains $n_1$ protons and $n_2$ electrons, the net charge on the object is

The radius of the first permitted Bohr orbit for the electron, in a hydrogen atom equals $0.51 \mathrm{\AA }$ and its ground state energy equals$- 13.6 \mathrm{eV}.$If the electron in the hydrogen atom is replaced by muon $\left({\mu }^{-1}\right)$) [Charge same as electron and mass $207 {\mathrm{m}}_{\mathrm{e}}$], the first Bohr radius and ground state energy will be

The minimum energy of an incident electron necessary for ionization of atom of hydrogen is equal to $W_0$. Find minimum initial energy $W (= a{W}_0)$ of singly ionized incident helium atom, necessary for ionization of stationary hydrogen atom.

The radius of inner most orbit of hydrogen atom is $5.3\times {10}^{-11} \mathrm{m}$. What is the radius of third allowed orbit of hydrogen atom?

The radius of $2^{\mathrm{nd}}$ orbit of ${\mathrm{He}}^{+}$ of Bohr's model is $r_1$ and that of fourth orbit of ${\mathrm{Be}}^{3+}$ is represented as $r_2.$ Now the ratio $\frac{r_2}{r_1}$ is $x:1.$ The value of $x$ is _____.

An atom absorbs a photon of wavelength $500 \mathrm{nm}$ and emits another photon of wavelength $600 \mathrm{nm}$. The net energy absorbed by the atom in this process is $n\times {10}^{-4}\mathrm{eV}$. The value of$n$is [Assume the atom to be stationary during the absorption and emission process] (Take $h=6.6\times {10}^{-34}\mathrm{J} \mathrm{s}$ $$ and $c=3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$ ).