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.

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.

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 energy of ${\mathrm{He}}^{+}$ ion in its first state is, (The ground state energy for the Hydrogen atom$-13.6 \mathrm{eV}$):

If in nature there may not be an element for which the whole principal quantum number $n>4$, then the total possible number of elements will be

The value of Rydberg's constant is

In third orbit of hydrogen atom wavelength of revolving electron is $\lambda .$ Calculate its circumference.