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.

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

The maximum wavelength of a photon which will ionize hydrogen atom is

plank's constant  $=6.634\times {10}^{-34} \mathrm{J} \mathrm{s}$

Charge of electron$=1.6\times {10}^{-19} \mathrm{C}$

Speed of light$=3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$

An electron in Bohr model of hydrogen atom absorbs a photon and gets excited to a state in which its angular momentum increases by $\frac{h}{\pi }$. Among the following, what may be the final energy of such an electron?

The circumference of the innermost orbit of a single electron Bohr atom is $3.33 \mathrm{Å}$ (Angstroms). The de Broglie wavelength of an electron in the $n=4$ orbit of hydrogen atom is

If the mass of the electron were$10$ times smaller, but the mass of the proton remained the same, then the radius of the first Bohr orbit in a hydrogen like atom would be

The longest wavelength of the Lyman series of the hydrogen atom spectrum is $\lambda$. Which of the following wavelengths also belong to the Lyman series?

The de-Broglie wavelength of the electron in the first Bohr orbit of the Hydrogen atom is equal to ( $a_B$ denotes the Bohr radius)

If we consider the electron (charge $=e$, mass$=m$ ) in the first Bohr orbit of a hydrogen atom as a small loop of current, then the magnitude of the magnetic dipole moment due to this current is

The ratio of the speed of the electron in the first Bohr orbit $\left(1s\right)$ of a hydrogen atom to that of the speed of light is approximately