Atoms

Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge $Ze$ are defined by their principal quantum number $n$, where $n\gg1$. Which of the following statement(s) is(are) true?

A hydrogen atom in its ground state is irradiated by light of wavelength 970 Å. Taking $hc/e=1.237\times10^{-6}$ eV m and the ground state energy of hydrogen atom as $-13.6$ eV, the number of lines present in the emission spectrum is

A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is :

A neutron moving with a speed '$v$' makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which inelastic collision will take place is :

Consider a hydrogen atom with its electron in the $n^{th}$ orbital. An electromagnetic radiation of wavelength 90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of $n$ is ($hc=1242$ eV nm)

An electron in an excited state of $\ce{Li^{2+}}$ ion has angular momentum $3h/2\pi$. The de Broglie wavelength of the electron in this state is $p\pi a_0$ (where $a_0$ is the Bohr radius). The value of $p$ is

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :

If one were to apply Bohr model to a particle of mass 'm' and charge 'q' moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the n$^{\text{th}}$ level will be :

The de - Broglie wavelength associated with the electron in the n = 4 level is :

If $\lambda_{Cu}$ is the wavelength of $K_\alpha$ X-ray line of copper (atomic number 29) and $\lambda_{Mo}$ is the wavelength of the $K_\alpha$ X-ray line of molybdenum (atomic number 42), then the ratio $\lambda_{Cu}/\lambda_{Mo}$ is close to

The radiation corresponding to $3\to2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3\times10^{-4}$ T. If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to :

Hydrogen $\left({}_1\mathrm H^1\right)$, Deuterium $\left({}_1\mathrm H^2\right)$, singly ionised Helium $\left({}_2\mathrm{He}^4\right)^+$ and doubly ionised lithium $\left({}_3\mathrm{Li}^6\right)^{++}$ all have one electron around the nucleus. Consider an electron transition from $n=2$ to $n=1$. If the wave lengths of emitted radiation are $\lambda_1$, $\lambda_2$, $\lambda_3$ and $\lambda_4$ respectively then approximately which one of the following is correct ?

If the binding energy of the electron in a hydrogen atom is 13.6 eV, the energy required to remove the electron from the first excited state of $\ce{Li^{++}}$ is :

Match List - I (Experiment performed) with List - II (Phenomena discovered/associated) and select the correct option from the options given below the lists :

The radius of the orbit of an electron in a Hydrogen-like atom is $4.5a_0$, where $a_0$ is the Bohr radius. Its orbital angular momentum is $\dfrac{3h}{2\pi}$. It is given that $h$ is Planck constant and $R$ is Rydberg constant. The possible wavelength(s), when the atom de-excites, is (are)

The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

A diatomic molecule has moment of inertia $I$. By Bohr's quantization condition its rotational energy in the $n^{\text{th}}$ level ($n=0$ is not allowed) is

It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to $\dfrac4\pi\times10^{11}$ Hz. Then the moment of inertia of CO molecule about its center of mass is close to (Take $h=2\pi\times10^{-34}$ J s)

Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?

The quantum number $n$ of the state finally populated in He⁺ ions is