Structure of Atom Quiz-1

The difference between the radii of \(3^{\text {rd }}\) and \(4^{\text {th }}\) orbits of \(\mathrm{Li}^{2+}\) is \(\Delta R_1\). The difference between the radii of \(3^{\text {rd }}\) and \(4^{\text {th }}\) orbits of \(\mathrm{He}^{+}\)is \(\Delta \mathrm{R}_2\). Ratio \(\Delta \mathrm{R}_1: \Delta \mathrm{R}_2\) is:

The region in the electromagnetic spectrum where the Balmer series lines appear is :

The shortest wavelength of \(\mathrm{H}\) atom in the Lyman series is \(\lambda_1\). The longest wavelength in the Balmer series is \(\mathrm{He}^{+}\)is :

For the Balmer series in the spectrum of \(\mathrm{H}\) atom, \(\bar{\nu}=R_H\left\{\frac{1}{n_1^2}-\frac{1}{n_2^2}\right\}\), the correct statements among (I) to (IV) are:
(I) As the wavelength decreases, the lines in the series converge
(II) The integer \(n_1\) is equal to 2
(III) The lines of the longest wavelength correspond to \(n_2=3\)
(IV) The ionization energy of hydrogen can be calculated from the wave number of these lines

The radius of the second Bohr orbit, in terms of the Bohr radius, \(a_0\), in \(\mathrm{Li}^{2+}\) is:

Among the following, the energy of \(2 s\) orbital is lowest in:

The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The spectral series are :

For any given series of spectral lines of atomic hydrogen, let \(\Delta \bar{\nu}=\bar{\nu}_{\max }-\bar{\nu}_{\min }\) be the difference in maximum and minimum frequencies in \(\mathrm{cm}^{-1}\). The ratio \(\Delta \bar{\nu}\) Lyman \(/ \Delta \bar{\nu}_{\text {Balmer }}\) is :

What is the work function of the metal if the light of wavelength \(4000\)Å generates photoelectrons of velocity \(6 \times 10^5 \mathrm{~ms}^{-1}\) from it ?
(Mass of electron \(=9 \times 10^{-31} \mathrm{~kg}\)
Velocity of light \(=3 \times 10^8 \mathrm{~ms}^{-1}\)
Planck’s constant \(=6.626 \times 10^{-34} \mathrm{Js}\)
Charge of electron \(=1.6 \times 10^{-19} \mathrm{JeV}^{-1}\) )

Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of \(\mathrm{H}\)-atom is suitable for this purpose?
\(
\left[R_H=1 \times 10^5 \mathrm{~cm}^{-1} \cdot \mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}, \mathrm{c}=3 \times 10^8 \mathrm{~ms}^{-1}\right]
\)

The ground state energy of hydrogen atom is \(-13.6 \mathrm{eV}\). The energy of second excited state of \(\mathrm{He}^{+}\)ion in \(\mathrm{eV}\) is:

Which of the following statements is false?

Ejection of the photoelectron from metal in the photoelectric effect experiment can be stopped by applying \(0.5 \mathrm{~V}\) when the radiation of \(250 \mathrm{~nm}\) is used. The work function of the metal is :

The radius of the second Bohr orbit for hydrogen atom is : (Plank’s const. \(h=6.6262 \times 10^{-34} \mathrm{Js}\); mass of electron \(=9.1091 \times 10^{-31} \mathrm{~kg}\); charge of electron \(\mathrm{e}=1.60210 \times 10^{-19} \mathrm{C}\); permittivity of vaccum \(\left.\in_0=8.854185 \times 10^{-12} \mathrm{~kg}^{-1} \mathrm{~m}^{-3} \mathrm{~A}^2\right)\)

If the shortest wavelength in Lyman series of hydrogen atom is A, then the longest wavelength in Paschen series of \(\mathrm{He}^{+}\)is :

A stream of electrons from a heated filaments was passed two charged plates kept at a potential difference \(\mathrm{V}\) esu. If ‘ \(\mathrm{e}\) ‘ and \(m\) are charge and mass of an electron, respectively, then the value of \(h / \lambda\) (where \(\lambda\) is wavelength associated with electron wave) is given by:

Which of the following is the energy of a possible excited state of hydrogen?

If \(m\) and \(e\) are the mass and charge of the revolving electron in the orbit of radius \(r\) for hydrogen atom, the total energy of the revolving electron will be:

If \(\lambda_0\) and \(\lambda\) be threshold wavelength and wavelength of incident light, the velocity of photoelectron ejected from the metal surface is:

Energy of an electron is given by \(\mathrm{E}=-2.178 \times 10^{-18} \mathrm{~J}\left(\frac{Z^2}{n^2}\right)\).
Wavelength of light required to excite an electron in an hydrogen atom from level \(n=1\) to \(n=2\) will be:
\(
\left(h=6.62 \times 10^{-34} \mathrm{Js} \text { and } \mathrm{c}=3.0 \times 10^8 \mathrm{~ms}^{-1}\right)
\)

The wave number of the first emission line in the Balmer series of \(\mathrm{H}\)-Spectrum is :
( \(\mathrm{R}=\) Rydberg constant \()\) :

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is \(\left[a_0\right.\) is Bohr radius \(]\) :

Given that the abundances of isotopes \({ }^{54} \mathrm{Fe},{ }^{56} \mathrm{Fe}\) and \({ }^{57} \mathrm{Fe}\) are \(5 \%, 90 \%\) and \(5 \%\), respectively, the atomic mass of \(\mathrm{Fe}\) is

The radius of which of the following orbit is same as that of the first Bohr’s orbit of hydrogen atom?

Rurtherford’s experiment, which established the nuclear model of the atom, used a beam of

Which of the following does not characterise X-rays?

The wavelength of a spectral line for an electronic transition is inversely related to :

The triad of nuclei that is isotonic is

The ratio of the energy of a photon of \(2000\)Å wavelength radiation to that of \(4000\)Å radiation is :

Rutherford’s alpha particle scattering experiment eventually led to the conclusion that :

Electromagnetic radiation with maximum wavelength is :

The radius of an atomic nucleus is of the order of :

Bohr model can explain :

Which electronic level would allow the hydrogen atom to absorb a photon but not to emit a photon?

The increasing order (lowest first) for the values of \(\mathrm{e} / \mathrm{m}\) (charge/mass) for electron \((e)\), proton \((p)\), neutron \((n)\) and alpha particle \((\alpha)\) is :

Rutherford’s scattering experiment is related to the size of the

Rutherford’s experiment on scattering of \(\alpha\)-particles showed for the first time that the atom has

The number of neutrons in dipositive zinc ion with mass number 70 is

The work function \((\varphi)\) of some metals is listed below. The number of metals which will show photoelectric effect when light of \(300 \mathrm{~nm}\) wavelength falls on the metal is

The figure that is not a direct manifestation of the quantum nature of atoms is :

The de Broglie wavelength of an electron in the \(4^{\text {th }}\) Bohr orbit is:

If \(p\) is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength \(\lambda\), then for \(1.5 p\) momentum of the photoelectron, the wavelength of the light should be:
(Assume the kinetic energy of ejected photoelectron to be very high in comparison to work function):

If the de Broglie wavelength of the electron in \(n^{\text {th }}\) Bohr orbit in a hydrogenic atom is equal to \(1.5 \pi \mathrm{a}_0\left(\mathrm{a}_0\right.\) is Bohr radius), then the value of \(\mathrm{n} / \mathrm{z}\) is :

The de-Broglie’s wavelength of electron present in first Bohr orbit of ‘H’ atom is:

At temperature \(\mathrm{T}\), the average kinetic energy of any particle is \(\frac{3}{2} \mathrm{kT}\). The de Broglie wavelength follows the order :

The de-Broglie wavelength of a particle of mass \(6.63 \mathrm{~g}\) moving with a velocity of \(100 \mathrm{~ms}^{-1}\) is:

The de Broglie wavelength of a car of mass \(1000 \mathrm{~kg}\) and velocity \(36 \mathrm{~km} / \mathrm{hr}\) is :

The wavelength associated with a golf ball weighing \(200 \mathrm{~g}\) and moving at a speed of \(5 \mathrm{~m} / \mathrm{h}\) is of the order

Which of the following relates to photons both as wave motion and as a stream of particles?

The work function of sodium metal is \(4.41 \times 10^{-19} \mathrm{~J}\). If photons of wavelength \(300 \mathrm{~nm}\) are incident on the metal, the kinetic energy of the ejected electrons will be ____ \(\times 10^{-21} \mathrm{~J}\).
\(
\left(h=6.63 \times 10^{-34} \mathrm{~J} \mathrm{~s} ; c=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)
\)