Atoms practice · Mixed difficulty

The ratio of ionization energy of Bohr’s hydrogen atom and Bohr’s hydrogen like lithium atom is

The path of scattered $\alpha$-particles is

In any Bohr orbit of the hydrogen atom, the ratio of kinetic energy to potential energy of the electron is

Assertion (A): In Rutherford experiment only few $\alpha-$ particles get rebounded.

Reason (R): Most of the atomic space is empty.

Statement-I: The trajectory traced by an incident particle depends on the impact parameter of collisions.

Statement-II: The impact parameter is the perpendicular distance of the initial velocity vector of the incident particle from the centre of the target nucleus.

Number of spectral lines in hydrogen atom is

Work required to pull an electron from helium atom is 40 eV. Then the work required to pull both the electrons from the helium atom is

The radiation emitted when an electron jumps from 4th orbit to 2nd orbit in hydrogen like atom is made to incident on a metal surface to produce photoelectrons. In this way the ejected electrons are made to enter into a uniform magnetic field of strength $\sqrt{5} \,\mathrm{mT}$ and perpendicular to the direction of motion of the electrons. In the field electrons move on a circular path of radius $4.55 \mathrm{~mm}$. If the work function of the metal is $1.1 \,\mathrm{eV}$, then
(a) Atomic number of the atom.
(b) Stopping potential of the photoelectrons. Find $a+b.$

Assertion (A): Electrons in the atom are held due to coulomb forces.
Reason (R): The atom is stable only because the centripetal force due to Coulomb's law is balanced by the centrifugal force.

According to Bohr model, the diameter of first orbit of hydrogen atom will be

Solid targets of different elements are bombarded by highly energetic electron beams. The frequency $\left( f \right)$ of the characteristic X-rays emitted from different targets varies with atomic number $Z$ as

The time period of electron in the ground state of hydrogen atom is three times the time period of the electron in the second excited state of a certain hydrogen like atom (atomic number $Z$). The value of $Z$ is

When an $\mathrm{\alpha }$ - particle of mass ‘m’ moving with the velocity ‘v’ bombards on a heavy nucleus of charge ‘Ze’, its distance of closest approach from the nucleus depends on m as:

Consider a hydrogen like atom whose energy in $\mathrm{n}^{\text {th }}$ excited state is given by

$E_n=-\frac{13.6}{n^2} Z^2$
when this excited atom makes a transition from an excited state to ground state. The most energetic photons have energy $\mathrm{E}_{\max }=52.224 \mathrm{eV}$ and the least energetic photons have energy $\mathrm{E}_{\min }=1.224 \mathrm{eV}$. Find the atomic number of atom.

Stopping potentials of $24,100,110,115 \mathrm{kV}$ are measured for photoelectrons emitted from a certain element when it is irradiated with monochromatic X-rays. The element is used as a target in an $\mathrm{X}$-ray tube. The energy of $\mathrm{K}$ line is -

An $\alpha$-particle after passing through a potential difference of $2 \times 10^6 \mathrm{~V}$ falls on a silver foil. The atomic number of silver is 47. Calculate (i) the kinetic energy of the $\alpha$-particle at the time of falling on the foil (ii) the kinetic energy of the $\alpha$-particle at a distance of $5 \times 10^{-14} \mathrm{~m}$ from the nucleus and (iii) the shortest distance from the nucleus of silver to which the $\alpha$-particle reaches.

In an atom for the electron to revolve around the nucleus, the necessary centripetal force is obtained from the following force exerted by the nucleus on the electron

In $X$-ray tube when the accelerating voltage $V$ is halved, the difference between the wavelength of ${K_\alpha }$ line and minimum wavelength of continuous $X$-ray spectrum

The extreme wavelengths of Paschen series are

An electron with kinetic energy $5\,\,eV$ is incident on a $H$-atom in its ground state. The collision

The first line of Balmer series has wavelength $6563\,\,{A^0}$. What will be the wavelength of the first member of Lyman series

The hydrogen atoms in its ground state are excited by means of monochromatic radiation of wavelength $1023 \mathop A\limits^ \circ$. The number of lines which can be seen in the resulting spectrum is:

The potential difference across Coolidge tube is $20 \mathrm{kv}$ and $10 \mathrm{~mA}$ current flows through the voltage supply. Only $0.5 \%$ of the energy carried by electrons striking the target is converted into X-ray. Then the power carried by X-ray beam in watts is -

The ratio of longest wavelength and the shortest wavelength observed in the five spectral series of emission spectrum of hydrogen is

For principal quantum number $n = 3$, the possible values of orbital quantum number $'l'$ are

The spectral series of the hydrogen atom that lies in the visible region of the electromagnetic spectrum

The absorption transitions between the first and the fourth energy states of hydrogen atom are $\mathrm{3}$. The emission transitions between these states will be

Assertion: Rayleigh scattering can be considered as elastic collisions of photons with massive particles.
Reason: In Rayleigh scattering, the energy of incident and scattered is same

The value of angular momentum for $\mathrm{He}^{+}$ ion in the first Bohr orbit is:

The impact parameter at which the scattering angle is ${90^\mathrm{o}},\,Z = 79$ and initial energy 10 MeV is