Bohr’s Theory of Hydrogen-Like Atoms

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 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

When the first transitions of the Balmer series of excited hydrogen atoms are observed at an angle $\theta =60°$ to their motion, the wavelength appears to be displaced by $\Delta \lambda =0.2Å$. If the velocity of the hydrogen atoms is found to be $\mathrm{N}\times {10}^3 \mathrm{m}{ \mathrm{s}}^{-1}$, then find the value of $\left[\mathrm{N}\right]$, where $\left[\right]$ is greatest integer function. [Take $R={10}^7{ \mathrm{m}}^{-1}$ ]

Two hydrogen like atoms $A$ and $B$ are of different masses and each atom contains equal no of protons and neutrons. When the atoms $A$ and $B$ moving with the same velocity strikes a heavy target, they rebound back with the same speed. In this process the atom $B$ imparts twice the momentum to the target than that $A$ imparts. Identify the atoms $A$ and $B$.

Work function of a metal $X$ equals the ionization energy of $L{i}^{2+}$ion in second excited state. Work function of another metal $Y$ equals the ionization energy of $H{e}^{+}$ion with electron in $n=4$. Now photons of energy$E$ fall separately on both the metals such that maximum kinetic energy of photoelectron emitted from metal $X$ is half that of photoelectron emitted from metal$Y$. Choose the correct statement ( $E_0=$ Potential energy of electron in ground state of hydrogen atom)

In hydrogen like atom $\left(Z=11\right)$, $n^{\mathrm{th}}$ line of Lyman series has wavelength $\lambda$ equal to the de-Broglie's wavelength of electron in the level from which it originated. The value of $n$ is

If the plank’s constant would be double the present value, in the Bohr’s model for hydrogen atom

The atomic number of element which has a $k_{\alpha }$ x-rays line of wavelength $1.8\dot{A}$ is.?