Bohr Model

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.

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.

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

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 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 _____.

The radius of fifth orbit of ${\mathrm{Li}}^{++}$ is$\mathrm{\_\_\_\_\_\_\_}\times {10}^{-12} \mathrm{m}.$ Take: radius of hydrogen atom$=0.51 \stackrel{\circ }{\mathrm{A}}$

The angular momentum for the electron in Bohr’s orbit is $L$. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be

A small particle of mass $m$ moves in such a way that its potential energy $U=\frac{1}{2}m{\omega }^2{r}^2$ where $\omega$ is constant and $r$ is the distance of the particle from origin. Assuming Bohr’s quantization of momentum and circular orbit, the radius of ${\mathrm{n}}^{\mathrm{th}}$ orbit will be proportional to

The energy of $H{e}^{+}$ in 2^nd orbit is $-13.6 \mathrm{eV}$ then energy of $B{e}^{+++}$ in $n=4$ is

A photon of energy $12.75 \mathrm{eV}$ falls on a H-atom. Find out the numbers of spectral lines observed.

An electron in its orbit undergoes transitions across the energy levels either by absorbing or emitting the photons. A given hydrogen atom is in third excited state.

Determine the final quantum number and the energy of the photon,
i. when a photon with shortest wavelength is emitted

ii. when a photon with longest wavelength is absorbed

Each of the statements below are based on the properties of electron orbits in a hydrogen atom.

Identify a statement that correctly satisfies the Bohr’s model of an atom.

In a hydrogen atom, the electron in a given orbit has total energy $-1.5 \mathrm{eV}$. The potential energy is