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## Numerical

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Consider an imaginary ion $${ }_{22}^{48} \mathrm{X}^{3-}$$. The nucleus contains '$$a$$'% more neutrons than the number...
JEE Main 2022 (Online) 26th July Evening Shift
The wavelength of an electron and a neutron will become equal when the velocity of the electron is $$x$$ times the veloc...
JEE Main 2022 (Online) 26th July Morning Shift
When the excited electron of a H atom from n = 5 drops to the ground state, the maximum number of emission lines observe...
JEE Main 2022 (Online) 25th July Evening Shift
The longest wavelength of light that can be used for the ionisation of lithium atom (Li) in its ground state is x $$\tim... JEE Main 2022 (Online) 25th June Morning Shift If the uncertainty in velocity and position of a minute particle in space are, 2.4$$\times$$10$$-$$26 (m s$$-$$1) and ... JEE Main 2022 (Online) 27th June Morning Shift Consider the following set of quantum numbers. .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:bl... JEE Main 2022 (Online) 27th June Evening Shift If the work function of a metal is 6.63$$\times$$10$$-$$19J, the maximum wavelength of the photon required to remove a... JEE Main 2022 (Online) 28th June Morning Shift A 50 watt bulb emits monochromatic red light of wavelength of 795 nm. The number of photons emitted per second by the bu... JEE Main 2021 (Online) 1st September Evening Shift The value of magnetic quantum number of the outermost electron of Zn+ ion is ______________. JEE Main 2021 (Online) 31st August Evening Shift Ge(Z = 32) in its ground state electronic configuration has x completely filled orbitals with ml = 0. The value of x is ... JEE Main 2021 (Online) 31st August Morning Shift The number of photons emitted by a monochromatic (single frequency) infrared range finder of power 1 mW and wavelength o... JEE Main 2021 (Online) 27th August Evening Shift The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to$${{{h^2}} \over {xma_0^2}}$$.... JEE Main 2021 (Online) 27th August Morning Shift A metal surface is exposed to 500 nm radiation. The threshold frequency of the metal for photoelectric current is 4.3$$...
JEE Main 2021 (Online) 26th August Evening Shift
An accelerated electron has a speed of 5 $$\times$$ 106 ms$$-$$1 with an uncertainty of 0.02%. The uncertainty in findin...
JEE Main 2021 (Online) 25th July Evening Shift
A source of monochromatic radiation of wavelength 400 nm provides 1000 J of energy in 10 seconds. When this radiation fa...
JEE Main 2021 (Online) 25th July Morning Shift
Number of electrons that Vanadium (Z = 23) has in p-orbitals is equal to _____________
JEE Main 2021 (Online) 22th July Evening Shift
The wavelength of electrons accelerated from rest through a potential difference of 40 kV is x $$\times$$ 10$$-$$12 m. T...
JEE Main 2021 (Online) 20th July Evening Shift
The Azimuthal quantum number for the valence electrons of Ga+ ion is ___________.(Atomic number of Ga = 31)...
JEE Main 2021 (Online) 20th July Morning Shift
In the ground state of atomic Fe(Z = 26), the spin-only magnetic moment is ____________ $$\times$$ 10$$-$$1 BM. (Round o...
JEE Main 2021 (Online) 17th March Evening Shift
A certain orbital has n = 4 and mL = $$-$$3. The number of radial nodes in this orbital is ____________. (Round off to t...
JEE Main 2021 (Online) 17th March Morning Shift
The number of orbitals with n = 5, m1 = +2 is ___________. (Round off to the Nearest Integer).
JEE Main 2021 (Online) 16th March Evening Shift
When light of wavelength 248 nm falls on a metal of threshold energy 3.0 eV, the de-Broglie wavelength of emitted electr...
JEE Main 2021 (Online) 16th March Morning Shift
A ball weighing 10 g is moving with a velocity of 90 ms$$-$$1. If the uncertainty in its velocity is 5%, then the uncert...
JEE Main 2021 (Online) 26th February Evening Shift
A proton and a Li3+ nucleus are accelerated by the same potential. If $$\lambda _{Li}$$ and $$\lambda _p$$ denote the de...
JEE Main 2021 (Online) 24th February Morning Slot
The work function of sodium metal is 4.41 $$\times$$ 10–19 J. If photons of wavelength 300 nm are incident on the meta...
JEE Main 2020 (Online) 2nd September Evening Slot

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Which of the following sets of quantum numbers is not allowed?
JEE Main 2022 (Online) 25th July Morning Shift
The number of radial nodes and total number of nodes in 4p orbital respectively are :
JEE Main 2022 (Online) 30th June Morning Shift
Consider the following pairs of electrons (A) (a) n = 3, $$l$$ = 1, m1 = 1, ms = + $${1 \over 2}$$ &nbsp;&nbsp;&nbsp;&nb...
JEE Main 2022 (Online) 24th June Morning Shift
The energy of one mole of photons of radiation of wavelength 300 nm is (Given : h = 6.63 $$\times$$ 10$$-$$34 J s, NA = ...
JEE Main 2022 (Online) 24th June Evening Shift
The pair, in which ions are isoelectronic with AI3+ is :
JEE Main 2022 (Online) 25th June Morning Shift
The minimum energy that must be possessed by photons in order to produce the photoelectric effect with platinum metal is...
JEE Main 2022 (Online) 25th June Evening Shift
The number of radial and angular nodes in 4d orbital are, respectively
JEE Main 2022 (Online) 26th June Evening Shift
If the radius of the 3rd Bohr's orbit of hydrogen atom is r3 and the radius of 4th Bohr's orbit is r4. Then :...
JEE Main 2022 (Online) 26th June Morning Shift
Consider the following statements : (A) The principal quantum number 'n' is a positive integer with values of 'n' = 1, 2...
JEE Main 2022 (Online) 28th June Evening Shift
Which of the following is the correct plot for the probability density $${\psi ^2}$$ (r) as a function of distance 'r' o...
JEE Main 2022 (Online) 29th June Evening Shift
Which of the following statements are correct? (A) The electronic configuration of Cr is [Ar] 3d5 4s1. (B) The magnetic ...
JEE Main 2022 (Online) 29th June Morning Shift
Given below are two statements.Statement I : According to Bohr's model of an atom, qualitatively the magnitude of veloci...
JEE Main 2021 (Online) 26th August Morning Shift
If the Thompson model of the atom was correct, then the result of Rutherford's gold foil experiment would have been :
JEE Main 2021 (Online) 27th July Evening Shift
Given below are two statements :Statement I : Rutherford's gold foil experiment cannot explain the line spectrum of hydr...
JEE Main 2021 (Online) 27th July Morning Shift
The spin only magnetic moments (in BM) for free Ti3+, V2+ and Sc3+ ions respectively are(At.No. Sc : 21, Ti : 22, V : 23...
JEE Main 2021 (Online) 25th July Evening Shift
Outermost electronic configuration of a group 13 element, E, is 4s2, 4p1. The electronic configuration of an element of ...
JEE Main 2021 (Online) 20th July Evening Shift
Given below are two statements :Statement I : Bohr's theory accounts for the stability and line spectrum of Li+ ion.Stat...
JEE Main 2021 (Online) 18th March Evening Shift
A certain orbital has no angular nodes and two radial nodes. The orbital is :
JEE Main 2021 (Online) 18th March Morning Shift
The ionic radius of Na+ ions is 1.02 $$\mathop A\limits^o$$. The ionic radii (in $$\mathop A\limits^o$$) of Mg2+ and A...
JEE Main 2021 (Online) 18th March Morning Shift
What is the spin-only magnetic moment value (BM) of a divalent metal ion with atomic number 25, in it's aqueous solution...
JEE Main 2021 (Online) 17th March Morning Shift
Which of the following forms of hydrogen emits low energy $$\beta$$- particles?
JEE Main 2021 (Online) 26th February Evening Shift
The orbital having two radial as well as two angular nodes is :
JEE Main 2021 (Online) 26th February Morning Shift
In which of the following pairs, the outer most electronic configuration will be the same?
JEE Main 2021 (Online) 25th February Morning Slot
The plots of radial distribution functions for various orbitals of hydrogen atom against 'r' are given below : The corre...
JEE Main 2021 (Online) 25th February Morning Slot
According to Bohr's atomic theory :(A) Kinetic energy of electron is $$\propto {{{Z^2}} \over {{n^2}}}$$.(B) The produc...
JEE Main 2021 (Online) 24th February Evening Slot
The correct statement about probability density (except at infinite distance from nucleus) is :
JEE Main 2020 (Online) 5th September Evening Slot
In the sixth period, the orbitals that are filled are :
JEE Main 2020 (Online) 5th September Morning Slot
The correct electronic configuration and spin-only magnetic moment (BM) of Gd3+ (Z = 64), respectively, are...
JEE Main 2020 (Online) 5th September Morning Slot
The difference between the radii of 3rd and 4th orbits of Li2+ is R1 . The difference between the radii of 3rd and 4th o...
JEE Main 2020 (Online) 5th September Morning Slot
The shortest wavelength of H atom in the Lyman series is $$\lambda$$1. The longest wavelength in the Balmar series of H...
JEE Main 2020 (Online) 4th September Evening Slot
The region in the electromagnetic spectrum where the Balmar series lines appear is :
JEE Main 2020 (Online) 4th September Morning Slot
The number of subshells associated with n = 4 and m = –2 quantum numbers is
JEE Main 2020 (Online) 2nd September Evening Slot
The figure that is not a direct manifestation of the quantum nature of atoms is :
JEE Main 2020 (Online) 2nd September Morning Slot
The de Broglie wavelength of an electron in the 4th Bohr orbit is :
JEE Main 2020 (Online) 9th January Morning Slot
Hydrogen has three isotopes (A), (B) and (C). If the number of neutron(s) in (A), (B) and (C) respectively, are (x), (y)...
JEE Main 2020 (Online) 8th January Evening Slot
The radius of the second Bohr orbit, in terms of the Bohr radius, a0, in Li2+ is :
JEE Main 2020 (Online) 8th January Evening Slot
For the Balmer series in the spectrum of H atom, $$\overline \nu = {R_H}\left\{ {{1 \over {n_1^2}} - {1 \over {n_2^2}}... JEE Main 2020 (Online) 8th January Morning Slot The number of orbitals associated with quantum number n = 5, ms = +$${1 \over 2}$$is : JEE Main 2020 (Online) 7th January Morning Slot The group number, number of valence electrons, and valency of an element with atomic number 15, respectively, are: JEE Main 2019 (Online) 12th April Morning Slot The electrons are more likely to be found : ... JEE Main 2019 (Online) 12th April Morning Slot The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The spectral se... JEE Main 2019 (Online) 10th April Evening Slot The graph between$${\left| \psi \right|^2}$$and r (radial distance) is shown below. This represents : ... JEE Main 2019 (Online) 10th April Morning Slot The isoelectronic set of ions is : JEE Main 2019 (Online) 10th April Morning Slot Consider the hydrated ions of Ti2+, V2+, Ti3+, and Sc3+. The correct order of their spin-only magnetic moments is : ... JEE Main 2019 (Online) 10th April Morning Slot Which one of the following about an electron occupying the 1s orbital in a hydrogen atom is incorrect ? (The Bohr radius... JEE Main 2019 (Online) 9th April Evening Slot For any given series of spectral lines of atomic hydrogen, let$$\Delta \mathop v\limits^\_ = \Delta {\overline v ...
JEE Main 2019 (Online) 9th April Morning Slot
If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having waveleng...
JEE Main 2019 (Online) 8th April Evening Slot
The quantum number of four electrons are given below : n = 4, l = 2, ml =–2, ms = –1/2 n = 3, l = 2, ml = 1, ms = +1/2 n...
JEE Main 2019 (Online) 8th April Morning Slot
The upper stratosphere consisting of the ozone layer protects us from sun's radiation that falls in the wavelength regio...
JEE Main 2019 (Online) 12th January Evening Slot
If the de Broglie wavelength of the electron in nth Bohr orbit in a hydrogenic atom is equal to 1.5 $$\pi$$a0 (a0 is Bo...
JEE Main 2019 (Online) 12th January Evening Slot
What is the work function of the metal if the light of wavelength 4000$$\mathop A\limits^ \circ$$ generates photoelect...
JEE Main 2019 (Online) 12th January Morning Slot
The de Broglie wavelength ($$\lambda$$) associated with a photoelectron varies with the frequency (v) of the incident r...
JEE Main 2019 (Online) 11th January Evening Slot
Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is suita...
JEE Main 2019 (Online) 11th January Morning Slot
The ground state energy of hydrogen atom is – 13.6 eV. The energy of second excited state of He+ ion in eV is : ...
JEE Main 2019 (Online) 10th January Evening Slot
Which of the following combination of statements is true regarding the interpretation of the atomic orbitals ? (a) An e...
JEE Main 2019 (Online) 9th January Evening Slot
For emission line of atomic hydrogen from ni = 8 to nf = n, the plot of wave number $$\left( {\overline v } \right)$$ ag...
JEE Main 2019 (Online) 9th January Morning Slot
The highest value of the calculated spin- only magnetic moment (in BM) among all the transition metal complexes is :
JEE Main 2019 (Online) 9th January Morning Slot
Which of the following statements is false ?
JEE Main 2018 (Online) 16th April Morning Slot
The de-Broglie's wavelength of electron present in first Bohr orbit of 'H' atom is :
JEE Main 2018 (Online) 15th April Evening Slot
Ejection of the photoelectron from metal in the photoelectric experiment can be stopped by applying 0.5 V when the radia...
JEE Main 2018 (Online) 15th April Morning Slot
The electron in the hydrogen atom undergoes transition from higher orbitals to orbital of radius 211.6 pm. This transiti...
JEE Main 2017 (Online) 9th April Morning Slot
If the shortest wavelength in Lyman series of hydrogen atom is A, then the longestwavelength in Paschen series of He+ is...
JEE Main 2017 (Online) 8th April Morning Slot
The group having isoelectronic species is:
JEE Main 2017 (Offline)
The radius of the second Bohr orbit for hydrogen atom is: (Planck’s Const. h = 6.6262 × 10-34 Js; mass of electron = 9.1...
JEE Main 2017 (Offline)
The total number of orbitals associated with the principal quantum number 5 is :
JEE Main 2016 (Online) 9th April Morning Slot
A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V esu....
JEE Main 2016 (Offline)
Which of the following is the energy of a possible excited state of hydrogen?
JEE Main 2015 (Offline)
The correct set of four quantum numbers for the valence elections of rubidium atom (Z= 37) is:
JEE Main 2014 (Offline)
Energy of an electron is given by $$E = - 2.178 \times {10^{ - 18}}J\left( {{{{Z^2}} \over {{n^2}}}} \right)$$. Wavelen...
JEE Main 2013 (Offline)
The electrons identified by quantum numbers n and l : (a) n = 4, $$l$$ = 1 (b) n = 4, $$l$$ = 0 (c) n = 3, $$l$$ = 2 (d...
AIEEE 2012
A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at :
AIEEE 2011
Ionisation energy of He+ is 19.6 x 10–18 J atom–1. The energy of the first stationary state (n = 1) of Li2+ is...
AIEEE 2010
The energy required to break one mole of Cl–Cl bonds in Cl2 is 242 kJ mol–1. The longest wavelength of light capable of ...
AIEEE 2010
In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. Certainity with which the position...
AIEEE 2009
Calculate the wavelength (in nanometer) associated with a proton moving at 1.0 x 103 ms−1 (Mass of proton = 1.67 $$\tim... AIEEE 2009 The ionization enthalpy of hydrogen atom is 1.312 × 106 J mol−1. The energy required to excite the electron in the atom ... AIEEE 2008 Which one of the following constitutes a group of the isoelectronic species? AIEEE 2008 Which of the following sets of quantum numbers represents the highest energy of an atom? AIEEE 2007 Which of the following sets of ions represents a collection of isoelectronic species? AIEEE 2006 Uncertainty in the position of an electron (mass = 9.1$$\times$$10-31 kg) moving with a velocity 300 ms-1, accurate up... AIEEE 2006 According to Bohr's theory, the angular momentum of an electron in 5th orbit is AIEEE 2006 Pick out the isoelectronic structure from the following :$$\eqalign{ &amp; \left( i \right)\,\,\,\,\,\,C{H_3}^ + \...
AIEEE 2005
In a multi-electron atom, which of the following orbitals described by the three quantum members will have the same ener...
AIEEE 2005
Of the following sets which one does NOT contain isoelectronic species?
AIEEE 2005
Which one of the following sets of ions represents the collection of isoelectronic species? (Atomic nos. : F = 9, Cl = 1...
AIEEE 2004
The wavelength of the radiation emitted when in a hydrogen atom electron falls from infinity to stationary state 1, woul...
AIEEE 2004
Consider the ground state of Cr atom (Z = 24). The number of electrons with the azimuthal quantum numbers, l = 1 and 2 a...
AIEEE 2004
Which of the following sets of quantum numbers is correct for an electron in 4f orbital?
AIEEE 2004
The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of 10 meters per second is approximately
AIEEE 2003
In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following ...
AIEEE 2003
Which one of the following groupings represents a collection of isoelectronic species? (At. nos. : Cs : 55, Br : 35)
AIEEE 2003
The orbital angular momentum for an electron revolving in an orbit is given by $$\sqrt {l(l + 1)} {h \over {2\pi }}$$. T...
AIEEE 2003
The number of d-electrons retained in Fe2+ (At no of Fe = 26) ion is
AIEEE 2003
In a hydrogen atom, if energy of an electron in ground state is -13.6 eV, then that in the 2nd excited state is...
AIEEE 2002
Uncertainty in position of a minute particle of mass 25 g in space is 10-5 m. What is the uncertainty in its velocity (i...
AIEEE 2002

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