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Given below are two statements:
Statement I : According to Bohr’s model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus.
Statement II : According to Bohr’s model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in principal quantum number.
In the light of the above statements, chose the most appropriate answer from the options given below:

A certain orbital has \( n = 4 \) and \( m_l = -3 \). The number of radial nodes in this orbital is ______. (Round off to the Nearest Integer).

If the Thompson model of the atom was correct, then the result of Rutherford’s foil experiment would have been:

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to \( \dfrac{h^{2}}{x m a_{0}^{2}} \). The value of \( 10x \) is __________. (\( a_{0} \) is radius of Bohr’s orbit) (Nearest integer) [Given: \( \pi = 3.14 \)]

What is the spin-only magnetic moment value (BM) of a divalent metal ion with atomic number \( 25 \), in it’s aqueous solutions?

A metal surface is exposed to \( 500 \, \text{nm} \) radiation. The threshold frequency of the metal for photoelectric current is \( 4.3 \times 10^{14} \, \text{Hz} \). The velocity of ejected electron is ________ \( \times 10^{5} \, \text{m s}^{-1} \). (Nearest integer)
[Use : \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( m_{e} = 9.0 \times 10^{-31} \, \text{kg} \) ]

\( \mathrm{Ge}\ (Z = 32) \) in its ground state electronic configuration has \( x \) completely filled orbitals with \( m_l = 0 \). The value of \( x \) is __________.

The value of magnetic quantum number of the outermost electron of \( \mathrm{Zn}^{+} \) ion is _____ . (Integer answer)

According to Bohr’s atomic theory:
(A) Kinetic energy of electron is \( \propto \dfrac{Z^2}{n^2} \).
(B) The product of velocity \( (v) \) of electron and principal quantum number \( (n) \), ‘\( vn \)’ \( \propto Z^2 \).
(C) Frequency of revolution of electron in an orbit is \( \propto \dfrac{Z^3}{n^3} \).
(D) Coulombic force of attraction on the electron is \( \propto \dfrac{Z^3}{n^4} \).
Choose the most appropriate answer from the options given below:

The number of photons emitted by a monochromatic (single frequency) infrared range finder of power \( 1 \,\mathrm{mW} \) and wavelength of \( 1000 \,\mathrm{nm} \), in \( 0.1 \) second is \( x \times 10^{13} \). The value of \( x \) is _______. (Nearest integer)
\( (h = 6.63 \times 10^{-34} \,\mathrm{J\,s}, \; c = 3.00 \times 10^{8} \,\mathrm{m\,s^{-1}}) \)

A \( 50 \) watt bulb emits monochromatic red light of wavelength of \( 795 \, \text{nm} \). The number of photons emitted per second by the bulb is \( x \times 10^{20} \). The value of \( x \) is:
[Given: \( h = 6.63 \times 10^{-34} \, \text{J s} \) and \( c = 3.0 \times 10^{8} \, \text{m s}^{-1} \)]

Given below are two statements :
Statement-I : Rutherford’s gold foil experiment cannot explain the line spectrum of hydrogen atom.
Statement-II : Bohr’s model of hydrogen atom contradicts Heisenberg’s uncertainly principle.
In the light of the above statements, choose the most appropriate answer from the options given below :

An accelerated electron has a speed of \( 5 \times 10^{6} \, \mathrm{m}\,\mathrm{s}^{-1} \) with an uncertainty of \( 0.02\% \). The uncertainty in finding its location while in motion is \( x \times 10^{-9} \, \mathrm{m} \). The value of \( x \) is _______. (Nearest integer)
[Use mass of electron \( = 9.1 \times 10^{-31} \, \mathrm{kg} \), \( h = 6.63 \times 10^{-34} \, \mathrm{J\,s} \), \( \pi = 3.14 \) ]

The Azimuthal quantum number for the valence electrons of \( \mathrm{Ga^+} \) ion is ______.
(Atomic number of \( \mathrm{Ga} = 31 \))

A source of monochromatic radiation of wavelength \( 400 \, \text{nm} \) provides \( 1000 \, \text{J} \) of energy in \( 10 \) seconds. When this radiation falls on the surface of sodium, \( x \times 10^{20} \) electrons are ejected per second. Assume that wavelength \( 400 \, \text{nm} \) is sufficient for ejection of electron from the surface of sodium metal. The value of \( x \) is ___________. (Nearest integer) \( (h = 6.626 \times 10^{-34} \, \text{J s}) \)

Given below are two statements:
Statement I: Bohr’s theory accounts for the stability and line spectrum of \( \text{Li}^+ \) ion.
Statement II: Bohr’s theory was unable to explain the splitting of spectral lines in the presence of a magnetic field.
In the light of the above statements, choose the most appropriate answer from the options given below:

The wavelength of electrons accelerated from rest through a potential difference of \( 40 \, \text{kV} \) is \( x \times 10^{-12} \, \text{m} \). The value of \( x \) is ____________. (Nearest integer)
Given: Mass of electron \( = 9.1 \times 10^{-31} \, \text{kg} \)
Charge on an electron \( = 1.6 \times 10^{-19} \, \text{C} \)
Plank’s constant \( = 6.63 \times 10^{-34} \, \text{Js} \)

A certain orbital has no angular nodes and two radial nodes. The orbital is:

The \( \mathrm{Eu^{2+}} \) ion is a strong reducing agent in spite of its ground state electronic configuration (outermost) : [Atomic number of Eu = \( 63 \)]

Number of electrons that Vanadium \( (Z = 23) \) has in \( p \)-orbitals is equal to _______.

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JEE Main 2021 31st August Morning Shift

\( \mathrm{Ge}\ (Z = 32) \) in its ground state electronic configuration has \( x \) completely filled orbitals with \( m_l = 0 \). The value of \( x \) is __________.