Structure of Atom
325 Questions
Start JEE Mains Test
2021
Q151
JEE Mains
Numerical
14 Mar 2026
A certain orbital has n = 4 and mL = $-$3. The number of radial nodes in this orbital is ____________. (Round off to the Nearest Integer).
Correct Answer: 0
Explanation:
Number of radial nodes = n – $\ell $ – 1
n = 4, mL =–3 so $\ell $ = 3
radial nodes = 4 – 3 – 1 = 0
n = 4, mL =–3 so $\ell $ = 3
radial nodes = 4 – 3 – 1 = 0
2021
Q152
JEE Mains
Numerical
14 Mar 2026
The number of orbitals with n = 5, m1 = +2 is ___________. (Round off to the Nearest Integer).
Correct Answer: 3
Explanation:
Given, n = 5, ml = + 2
For n = 5, possible value of l = 0, 1, 2, 3, 4
For l = 0, ml = 0
l = 1, ml = $-$1, 0, 1
l = 2, ml = $-$2, $-$1, 0, 1, 2
l = 3, ml = $-$3, $-$2, $-$1, 0, 1, 2, 3
l = 4, ml = $-$4, $-$3, $-$2, $-$1, 0, 1, 2, 3, 4
Possible value of ml for a given value of l
= 0, $\pm$ 1, $\pm$ 2, $\pm$ 3 ..... $\pm$ l
So, number of orbitals having n = 5 and ml = $\pm$ 2 are 3.
2021
Q153
JEE Mains
Numerical
14 Mar 2026
When light of wavelength 248 nm falls on a metal of threshold energy 3.0 eV, the de-Broglie wavelength of emitted electrons is _______$\mathop A\limits^o $. (Round off to the Nearest Integer).
[ Use : $\sqrt 3 $ = 1.73, h = 6.63 $\times$ 10$-$34 Js
me = 9.1 $\times$ 10$-$31 kg; c = 3.0 $\times$ 108 ms$-$1; 1eV = 1.6 $\times$ 10$-$19 J]
[ Use : $\sqrt 3 $ = 1.73, h = 6.63 $\times$ 10$-$34 Js
me = 9.1 $\times$ 10$-$31 kg; c = 3.0 $\times$ 108 ms$-$1; 1eV = 1.6 $\times$ 10$-$19 J]
Correct Answer: 9
Explanation:
$\lambda$ = 248 $\times$ 10$-$9 m
w0 = 3 $\times$ 1.6 $\times$ 10$-$19 J
E = w0 + K.E.
${{hc} \over \lambda } = {W_0} + K.E.$
$K.E. = {{6.626 \times {{10}^{ - 34}} \times 3 \times {{10}^8}} \over {248 \times {{10}^{ - 19}}}} - 3 \times 1.6 \times {10^{ - 19}}$
= 3.2 $\times$ 10$-$19 J
p = $\sqrt {2mK.E.} $
p = $\sqrt {2 \times 9.1 \times {{10}^{ - 31}} \times 3.2 \times {{10}^{ - 19}}} $
p = 7.63 $\times$ 10$-$25
$ \therefore $ $\lambda = {h \over p} = {{6.626 \times {{10}^{ - 34}}} \over {7.63 \times {{10}^{ - 25}}}}$
$ \Rightarrow $ $\lambda$ = 8.7 $\times$ 10$-$10 = 8.7 $\mathop A\limits^o $ $ \approx $ 9 $\mathop A\limits^o $
w0 = 3 $\times$ 1.6 $\times$ 10$-$19 J
E = w0 + K.E.
${{hc} \over \lambda } = {W_0} + K.E.$
$K.E. = {{6.626 \times {{10}^{ - 34}} \times 3 \times {{10}^8}} \over {248 \times {{10}^{ - 19}}}} - 3 \times 1.6 \times {10^{ - 19}}$
= 3.2 $\times$ 10$-$19 J
p = $\sqrt {2mK.E.} $
p = $\sqrt {2 \times 9.1 \times {{10}^{ - 31}} \times 3.2 \times {{10}^{ - 19}}} $
p = 7.63 $\times$ 10$-$25
$ \therefore $ $\lambda = {h \over p} = {{6.626 \times {{10}^{ - 34}}} \over {7.63 \times {{10}^{ - 25}}}}$
$ \Rightarrow $ $\lambda$ = 8.7 $\times$ 10$-$10 = 8.7 $\mathop A\limits^o $ $ \approx $ 9 $\mathop A\limits^o $
2021
Q154
JEE Mains
Numerical
14 Mar 2026
A ball weighing 10 g is moving with a velocity of 90 ms$-$1. If the uncertainty in its velocity is 5%, then the uncertainty in its position is ___________ $\times$ 10$-$33 m. (Rounded off to the nearest integer)
[Given : h = 6.63 $\times$ 10$-$34 Js]
[Given : h = 6.63 $\times$ 10$-$34 Js]
Correct Answer: 1
Explanation:
m = 10 g = 10$-$2 Kg
v = 90 m/sec.
$\Delta$ = v $\times$ 5% = 90 $\times$ ${5 \over {100}}$ = 4.5 m/sec
m . $\Delta$v . $\Delta$x $ \ge $ ${h \over {4\pi }}$
10$-$2 $\times$ 4.5 $\times$ $\Delta$x $ \ge $ ${{6.63 \times 3 \times {{10}^{ - 34}}} \over {4 \times {{22} \over 7}}}$
$\Delta$x $ \ge $ ${{6.63 \times 7 \times 2 \times {{10}^{ - 34}}} \over {9 \times 4 \times 22 \times {{10}^{ - 2}}}}$
$\Delta$x $ \ge $ 1.17 $\times$ 10$-$33 = x $\times$ 10$-$33
x = 1.17 $ \simeq $ 1
v = 90 m/sec.
$\Delta$ = v $\times$ 5% = 90 $\times$ ${5 \over {100}}$ = 4.5 m/sec
m . $\Delta$v . $\Delta$x $ \ge $ ${h \over {4\pi }}$
10$-$2 $\times$ 4.5 $\times$ $\Delta$x $ \ge $ ${{6.63 \times 3 \times {{10}^{ - 34}}} \over {4 \times {{22} \over 7}}}$
$\Delta$x $ \ge $ ${{6.63 \times 7 \times 2 \times {{10}^{ - 34}}} \over {9 \times 4 \times 22 \times {{10}^{ - 2}}}}$
$\Delta$x $ \ge $ 1.17 $\times$ 10$-$33 = x $\times$ 10$-$33
x = 1.17 $ \simeq $ 1
2021
Q155
JEE Mains
Numerical
14 Mar 2026
Electromagnetic radiation of wavelength 663 nm is just sufficient to ionise the atom of metal A. The ionization enegy of metal A in kJ mol$-$1 is __________. (Rounded off to the nearest integer)
[h = 6.63 $\times$ 10$-$34 Js, c = 3.00 $\times$ 108 ms$-$1, NA = 6.02 $\times$ 1023 mol$-$1]
[h = 6.63 $\times$ 10$-$34 Js, c = 3.00 $\times$ 108 ms$-$1, NA = 6.02 $\times$ 1023 mol$-$1]
Correct Answer: 181
Explanation:
Energy of EMR = IE of the metal (A)
$ = hv = {{hc} \over \lambda }$ atom$-$1 $ = {{hc} \over \lambda } \times {N_A}$ mol$-$1
$ = {{(6.63 \times {{10}^{ - 34}}) \times (3 \times {{10}^8}) \times (6.02 \times {{10}^{23}})} \over {(663 \times {{10}^{ - 9}})}}$ J mol$-$1 [$\because$ $\lambda$ = 663 nm = 663 $\times$ 10$-$9 m]
= 180600 J mol$-$1 = 180.6 kJ mol$-$1 $ \simeq $ 181 kJ mol$-$1
2021
Q156
JEE Mains
Numerical
14 Mar 2026
Among the following, number of metal/s which can be used as electrodes in the photoelectric cell is _________. (Integer answer)
(A) Li
(B) Na
(C) Rb
(D) Cs
(A) Li
(B) Na
(C) Rb
(D) Cs
Correct Answer: 1
Explanation:
Among the given alkali metals, only cesium (Cs)
is used as electrode in the photoelectric cell
due to its lowest ionisation energy.
2021
Q157
JEE Mains
Numerical
14 Mar 2026
A proton and a Li3+ nucleus are accelerated by the same potential. If $\lambda _{Li}$ and $\lambda _p$ denote the
de Broglie wavelengths of Li3+ and proton respectively, then the value of
${{{\lambda _{Li}}} \over {{\lambda _p}}}$ is x $ \times $ 10-1.
The value of x is ______. (Rounded off to the nearest integer)
[Mass of Li3+ = 8.3 mass of proton]
The value of x is ______. (Rounded off to the nearest integer)
[Mass of Li3+ = 8.3 mass of proton]
Correct Answer: 2
Explanation:
Given, mass of Li3+ = 8.3 times of mass of proton formula,
De-Broglie wavelength, $\lambda = {h \over {\sqrt {2mqV} }}$
Here, h = Planck's constant = 6.624 $\times$ 10$-$34 J-s
m = Mass of atom
q = Charge (or number of electrons)
${\lambda _{Li}} = {h \over {\sqrt {2{m_{Li}}(3e)v} }}$ .... (i)
${\lambda _P} = {h \over {\sqrt {2{m_P}(e)v} }}$ .... (ii)
Now, Eq. (i) divided by Eq. (ii), we get,
${{{\lambda _{Li}}} \over {{\lambda _P}}} = \sqrt {{{{m_P}(e)v} \over {{m_{Li}}(3e)v}}} $
We know that mLi = 8.3 mp
${{{\lambda _{Li}}} \over {{\lambda _P}}} = \sqrt {{{{m_P} \times e \times V} \over {8.3\,{m_P} \times 3e \times V}}} = \sqrt {{1 \over {8.3 \times 3}}} = {1 \over 5} = 0.2$ = 2 $\times$ 10$-$1
Hence, x $\times$ 10$-$1, x = 2
De-Broglie wavelength, $\lambda = {h \over {\sqrt {2mqV} }}$
Here, h = Planck's constant = 6.624 $\times$ 10$-$34 J-s
m = Mass of atom
q = Charge (or number of electrons)
${\lambda _{Li}} = {h \over {\sqrt {2{m_{Li}}(3e)v} }}$ .... (i)
${\lambda _P} = {h \over {\sqrt {2{m_P}(e)v} }}$ .... (ii)
Now, Eq. (i) divided by Eq. (ii), we get,
${{{\lambda _{Li}}} \over {{\lambda _P}}} = \sqrt {{{{m_P}(e)v} \over {{m_{Li}}(3e)v}}} $
We know that mLi = 8.3 mp
${{{\lambda _{Li}}} \over {{\lambda _P}}} = \sqrt {{{{m_P} \times e \times V} \over {8.3\,{m_P} \times 3e \times V}}} = \sqrt {{1 \over {8.3 \times 3}}} = {1 \over 5} = 0.2$ = 2 $\times$ 10$-$1
Hence, x $\times$ 10$-$1, x = 2
2021
Q158
JEE Advanced
Numerical
14 Mar 2026
Consider a helium (He) atom that absorbs a photon of wavelength 330 nm. The change in the velocity (in cm s$-$1) of He atom after the photon absorption is __________.
(Assume : Momentum is conserved when photon is absorbed.
Use : Planck constant = 6.6 $\times$ 10$-$34 J s, Avogadro number = 6 $\times$ 1023 mol$-$1, Molar mass of He = 4 g mol$-$1)
(Assume : Momentum is conserved when photon is absorbed.
Use : Planck constant = 6.6 $\times$ 10$-$34 J s, Avogadro number = 6 $\times$ 1023 mol$-$1, Molar mass of He = 4 g mol$-$1)
Correct Answer: 30
Explanation:
Wavelength of photon absorbed, $\lambda$ = 330 nm = 330 $\times$ 10$-$9 m
Planck's constant, h = 6.6 $\times$ 10$-$34 J s
Molar mass of He, M = 4 g mol$-$1 = 4 $\times$ 10$-$3 kg mol$-$1
Avogadro number, NA = 6 $\times$ 1023 mol$-$1
Mass of one atom of He, $m = {M \over {{N_A}}}$
$ = {{4 \times {{10}^{ - 3}}} \over {6 \times {{10}^{23}}}} = {2 \over 3} \times {10^{ - 26}}$ kg
Velocity, = V cm/s.
Using de-Broglie equation,
$\lambda = {h \over {mv}}$
$ \Rightarrow v = {h \over {m\lambda }} = {{6.6 \times {{10}^{ - 34}}} \over {2/3 \times {{10}^{ - 26}} \times 330 \times {{10}^{ - 9}}}}$
$ = {{6.6 \times 3 \times {{10}^{ - 34}} \times {{10}^{35}}} \over {2 \times 330}} = 0.03 \times 10 = 0.3$ m/s
= 30 cm/s
Planck's constant, h = 6.6 $\times$ 10$-$34 J s
Molar mass of He, M = 4 g mol$-$1 = 4 $\times$ 10$-$3 kg mol$-$1
Avogadro number, NA = 6 $\times$ 1023 mol$-$1
Mass of one atom of He, $m = {M \over {{N_A}}}$
$ = {{4 \times {{10}^{ - 3}}} \over {6 \times {{10}^{23}}}} = {2 \over 3} \times {10^{ - 26}}$ kg
Velocity, = V cm/s.
Using de-Broglie equation,
$\lambda = {h \over {mv}}$
$ \Rightarrow v = {h \over {m\lambda }} = {{6.6 \times {{10}^{ - 34}}} \over {2/3 \times {{10}^{ - 26}} \times 330 \times {{10}^{ - 9}}}}$
$ = {{6.6 \times 3 \times {{10}^{ - 34}} \times {{10}^{35}}} \over {2 \times 330}} = 0.03 \times 10 = 0.3$ m/s
= 30 cm/s
2020
Q159
JEE Mains
MCQ
14 Mar 2026
The correct statement about probability density (except at infinite distance from nucleus) is :
A.
It can be zero for 1s orbital
B.
It can be zero for 3p orbital
C.
It can never be zero for 2s orbital
D.
It can negative for 2p orbital
2020
Q160
JEE Mains
MCQ
14 Mar 2026
The difference between the radii of 3rd and 4th
orbits of Li2+ is R1 . The difference between the
radii of 3rd and 4th orbits of He+ is $\Delta $R2 .
Ratio $\Delta $R1 : $\Delta $R2 is :
orbits of Li2+ is R1 . The difference between the
radii of 3rd and 4th orbits of He+ is $\Delta $R2 .
Ratio $\Delta $R1 : $\Delta $R2 is :
A.
8 : 3
B.
3 : 2
C.
2 : 3
D.
3 : 8
2020
Q161
JEE Mains
MCQ
14 Mar 2026
The shortest wavelength of H atom in the
Lyman series is $\lambda $1. The longest wavelength in
the Balmar series of He+ is :
A.
${{5{\lambda _1}} \over 9}$
B.
${{36{\lambda _1}} \over 5}$
C.
${{27{\lambda _1}} \over 5}$
D.
${{9{\lambda _1}} \over 5}$
2020
Q162
JEE Mains
MCQ
14 Mar 2026
The region in the electromagnetic spectrum
where the Balmar series lines appear is :
A.
Microwave
B.
Ultraviolet
C.
Visible
D.
Infrared
2020
Q163
JEE Mains
MCQ
14 Mar 2026
Consider the hypothetical situation where the
azimuthal quantum number,
$l$, takes values 0,
1, 2, ....., n + 1, where n is the principal
quantum number. Then, the element with
atomic number :
A.
13 has a half-filled valence subshell
B.
9 is the first alkali metal
C.
8 is the first noble gas
D.
6 has a 2p-valence subshell
2020
Q164
JEE Mains
MCQ
14 Mar 2026
The number of subshells associated with n = 4
and m = –2 quantum numbers is
A.
8
B.
2
C.
16
D.
4
2020
Q165
JEE Mains
MCQ
14 Mar 2026
The figure that is not a direct manifestation of
the quantum nature of atoms is :
A.
B.
C.
D.
2020
Q166
JEE Mains
MCQ
14 Mar 2026
The de Broglie wavelength of an electron in the
4th Bohr orbit is :
A.
2$\pi $a0
B.
6$\pi $a0
C.
8$\pi $a0
D.
4$\pi $a0
2020
Q167
JEE Mains
MCQ
14 Mar 2026
The radius of the second Bohr orbit, in terms
of the Bohr radius, a0, in Li2+ is :
A.
${{2{a_0}} \over 9}$
B.
${{2{a_0}} \over 3}$
C.
${{4{a_0}} \over 9}$
D.
${{4{a_0}} \over 3}$
2020
Q168
JEE Mains
MCQ
14 Mar 2026
Hydrogen has three isotopes (A), (B) and (C).
If the number of neutron(s) in (A), (B) and (C)
respectively, are (x), (y) and (z), the sum of (x),
(y) an (z) is :
A.
3
B.
1
C.
4
D.
2
2020
Q169
JEE Mains
MCQ
14 Mar 2026
For the Balmer series in the spectrum of H atom,
$\overline \nu = {R_H}\left\{ {{1 \over {n_1^2}} - {1 \over {n_2^2}}} \right\}$, the correct statements among (I) to (IV) are :
(I) As wavelength decreases, the lines in the series converge
(II) The integer n1 is equal to 2
(III) The lines of longest wavelength corresponds to n2 = 3
(IV) The ionization energy of hydrogen can be calculated from wave number of these lines
$\overline \nu = {R_H}\left\{ {{1 \over {n_1^2}} - {1 \over {n_2^2}}} \right\}$, the correct statements among (I) to (IV) are :
(I) As wavelength decreases, the lines in the series converge
(II) The integer n1 is equal to 2
(III) The lines of longest wavelength corresponds to n2 = 3
(IV) The ionization energy of hydrogen can be calculated from wave number of these lines
A.
(II), (III), (IV)
B.
(I), (II), (III)
C.
(I), (III), (IV)
D.
(I), (II), (IV)
2020
Q170
JEE Mains
MCQ
14 Mar 2026
The number of orbitals associated with quantum number n = 5, ms = +${1 \over 2}$ is :
A.
11
B.
25
C.
15
D.
50
2020
Q171
JEE Mains
Numerical
14 Mar 2026
The work function of sodium metal is
4.41 $ \times $ 10–19 J. If photons of wavelength 300 nm
are incident on the metal, the kinetic energy of
the ejected electrons will be (h = 6.63 $ \times $ 10–34 J s;
c = 3 $ \times $ 108 m/s) ________ × 10–21 J.
Correct Answer: 222
Explanation:
E = W + KEmax
$ \Rightarrow $ KEmax = E - W
= ${{hc} \over \lambda }$ - 4.41 $ \times $ 10–19
= ${{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}} \over {300 \times {{10}^{ - 9}}}}$ - 4.41 $ \times $ 10–19
= 2.22 × 10–19 J
= 222 × 10–21 J
$ \Rightarrow $ KEmax = E - W
= ${{hc} \over \lambda }$ - 4.41 $ \times $ 10–19
= ${{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}} \over {300 \times {{10}^{ - 9}}}}$ - 4.41 $ \times $ 10–19
= 2.22 × 10–19 J
= 222 × 10–21 J
2020
Q172
JEE Advanced
Numerical
14 Mar 2026
The figure below is the plot of potential energy versus internuclear distance (d) of H2 molecule in the electronic ground state. What is the value of the net potential energy E0 (as indicated in the figure) in kJ mol-1, for d = d0 at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent? As reference, the potential energy of H atom is taken as zero when its electron and the nucleus are infinitely far apart.
Use Avogadro constant as 6.023 $ \times $ 1023 mol-1.
Use Avogadro constant as 6.023 $ \times $ 1023 mol-1.
Correct Answer: $$-$$5242.41
Explanation:
Given that, electrons and nucleus are at infinite distance, so potential energy of H-atom is taken as zero.
Therefore, according to Bohr's model, potential energy of a H-atom with electron in its ground state = $-$27.2 eV
At d = d0, nucleus-nucleus and electron-electron repulsion is absent.
Hence, potential energy will be calculated for 2 H atoms = $-$2 $ \times $ 27.2 eV = $-$54.4 eV
Potential energy of 1 mol H atoms in kJ
= ${{54.4 \times 6.02 \times {{10}^{23}} \times 1.6 \times {{10}^{ - 19}}} \over {1000}}$
= $ - 5242.4192$ kJ/mol
Therefore, according to Bohr's model, potential energy of a H-atom with electron in its ground state = $-$27.2 eV
At d = d0, nucleus-nucleus and electron-electron repulsion is absent.
Hence, potential energy will be calculated for 2 H atoms = $-$2 $ \times $ 27.2 eV = $-$54.4 eV
Potential energy of 1 mol H atoms in kJ
= ${{54.4 \times 6.02 \times {{10}^{23}} \times 1.6 \times {{10}^{ - 19}}} \over {1000}}$
= $ - 5242.4192$ kJ/mol
2019
Q173
JEE Mains
MCQ
14 Mar 2026
The electrons are more likely to be found :
A.
only in the region a
B.
in the region a arid c
C.
only in the region c
D.
in the region a and b
2019
Q174
JEE Mains
MCQ
14 Mar 2026
The group number, number of valence electrons, and valency of an element with atomic number 15,
respectively, are:
A.
16, 6 and 3
B.
15, 6 and 12
C.
16, 5 and 2
D.
15, 5 and 3
2019
Q175
JEE Mains
MCQ
14 Mar 2026
The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The
spectral series are :
A.
Paschen and Pfund
B.
Balmer and Brackett
C.
Lyman and Paschen
D.
Brackett and Pfund
2019
Q176
JEE Mains
MCQ
14 Mar 2026
The graph between ${\left| \psi \right|^2}$ and r (radial distance) is shown below. This represents :
A.
3s orbital
B.
2s orbital
C.
2p orbital
D.
1s orbital
2019
Q177
JEE Mains
MCQ
14 Mar 2026
The isoelectronic set of ions is :
A.
F–, Li+, Na+ and Mg2+
B.
Li+, Na+, O2- and F-
C.
N3–, O2-, F- and Na+
D.
N3–, Li+, Mg2+ and O2-
2019
Q178
JEE Mains
MCQ
14 Mar 2026
Which one of the following about an electron
occupying the 1s orbital in a hydrogen atom is
incorrect ?
(The Bohr radius is represented by a0)
(The Bohr radius is represented by a0)
A.
The probability density of finding the
electron is maximum at the nucleus.
B.
The electron can be found at a distance 2a0
from the nucleus
C.
The total energy of the electron is maximum
when it is at a distance a0 from the nucleus.
D.
The magnitude of potential energy is
double that of its kinetic energy on an
average.
2019
Q179
JEE Mains
MCQ
14 Mar 2026
For any given series of spectral lines of atomic
hydrogen, let $\Delta \mathop v\limits^\_ = $ $\Delta {\overline v _{\max }} - \Delta {\overline v _{\min }}$ be the difference
in maximum and minimum frequencies in
cm–1. The ratio Lyman Balmer ${{\Delta {{\overline v }_{Lyman}}} \over {\Delta {{\overline v }_{Balmer}}}}$ is :
A.
9 : 4
B.
4 : 1
C.
27 : 5
D.
5 : 4
2019
Q180
JEE Mains
MCQ
14 Mar 2026
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 kinetic energy of ejected
photoelectron to be very high in comparison
to work function)
A.
1/2 $\lambda $
B.
3/4 $\lambda $
C.
4/9 $\lambda $
D.
2/3 $\lambda $
2019
Q181
JEE Mains
MCQ
14 Mar 2026
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 = 4, l = 1, ml = 0, ms = +1/2
n = 3, l = 1, ml = 1, ms = –1/2
The correct order of their increasing enegies will be :
n = 4, l = 2, ml =–2, ms = –1/2
n = 3, l = 2, ml = 1, ms = +1/2
n = 4, l = 1, ml = 0, ms = +1/2
n = 3, l = 1, ml = 1, ms = –1/2
The correct order of their increasing enegies will be :
A.
IV < II < III < I
B.
I < III < II < IV
C.
IV < III < II < I
D.
I < II < III < IV
2019
Q182
JEE Mains
MCQ
14 Mar 2026
If the de Broglie wavelength of the electron in nth Bohr orbit in a hydrogenic atom is equal to 1.5 $\pi $a0 (a0 is Bohr radius), then the value of n/z is -
A.
0.75
B.
0.40
C.
1.50
D.
1.0
2019
Q183
JEE Mains
MCQ
14 Mar 2026
The upper stratosphere consisting of the ozone layer protects us from sun's radiation that falls in the wavelength region of -
A.
200-315 nm
B.
400-550 nm
C.
0.8-1.5 nm
D.
600-750 nm
2019
Q184
JEE Mains
MCQ
14 Mar 2026
What is the work function of the metal if the light of wavelength 4000$\mathop A\limits^ \circ $ generates photoelectrons of velocity 6 $ \times $ 105 ms–1 from it ?
(Mass of electron = 9 $ \times $ 10–31 kg;
Velocity of light = 3 $ \times $ 108 ms$-$1
Plank's constant = 6.626 $ \times $ 10–34 Js;
Charge of electron = 1.6 $ \times $10–19 JeV–1)
(Mass of electron = 9 $ \times $ 10–31 kg;
Velocity of light = 3 $ \times $ 108 ms$-$1
Plank's constant = 6.626 $ \times $ 10–34 Js;
Charge of electron = 1.6 $ \times $10–19 JeV–1)
A.
4.0 eV
B.
0.9 eV
C.
2.1 eV
D.
3.1 eV
2019
Q185
JEE Mains
MCQ
14 Mar 2026
The de Broglie wavelength ($\lambda $) associated with a photoelectron varies with the frequency (v) of the incident radiation as, [v0 is threshold frequency] :
A.
$\lambda \,\infty \,{1 \over {{{\left( {v - {v_0}} \right)}^{{3 \over 2}}}}}$
B.
$\lambda \,\infty \,{1 \over {{{\left( {v - {v_0}} \right)}^{{1 \over 4}}}}}$
C.
$\lambda \,\infty \,{1 \over {\left( {v - {v_0}} \right)}}$
D.
$\lambda \,\infty \,{1 \over {{{\left( {v - {v_0}} \right)}^{{1 \over 2}}}}}$
2019
Q186
JEE Mains
MCQ
14 Mar 2026
Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is suitable for this purpose?
[RH = 1 $ \times $ 105 cm–1, h = 6.6 $ \times $ 10–34 Js, c = 3 $ \times $ 108 ms–1]
[RH = 1 $ \times $ 105 cm–1, h = 6.6 $ \times $ 10–34 Js, c = 3 $ \times $ 108 ms–1]
A.
Balmer, $\infty $ $ \to $ 2
B.
Paschen, 5 $ \to $ 3
C.
Paschen, $\infty $ $ \to $ 3
D.
Lyman, $\infty $ $ \to $ 1
2019
Q187
JEE Mains
MCQ
14 Mar 2026
The ground state energy of hydrogen atom is – 13.6 eV. The energy of second excited state of He+ ion in eV is :
A.
$-$ 6.04
B.
$-$ 54.4
C.
$-$ 27.2
D.
$-$ 3.4
2019
Q188
JEE Mains
MCQ
14 Mar 2026
Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from metal surface ?
A.
B.
C.
D.
2019
Q189
JEE Mains
MCQ
14 Mar 2026
Which of the following combination of statements is true regarding the interpretation of the atomic orbitals ?
(a) An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum.
(b) For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number.
(c) According to wave mechanics, the ground state angular momentum is equal to ${h \over {2\pi }}$.
(d) The plot of $\psi $ vs r for various azimuthal quantum numbers, shows peak shifting towards higher r value.
(a) An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum.
(b) For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number.
(c) According to wave mechanics, the ground state angular momentum is equal to ${h \over {2\pi }}$.
(d) The plot of $\psi $ vs r for various azimuthal quantum numbers, shows peak shifting towards higher r value.
A.
(a), (b)
B.
(a), (d)
C.
(b), (c)
D.
(a), (c)
2019
Q190
JEE Mains
MCQ
14 Mar 2026
The highest value of the calculated spin only magnetic moment (in BM) among all the transition metal complexes is :
A.
5.92
B.
6.93
C.
3.87
D.
4.90
2019
Q191
JEE Mains
MCQ
14 Mar 2026
For emission line of atomic hydrogen from ni = 8 to nf = n, the plot of wave number $\left( {\overline v } \right)$ against $\left( {{1 \over {{n^2}}}} \right)$ will be (The Rydberg constant, RH is in wave number unit)
A.
Linear with intercept $-$RH
B.
Non linear
C.
Linear with slope RH
D.
Linear with slope $-$RH
2019
Q192
JEE Advanced
MCQ
14 Mar 2026
Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the nth orbit of the atom and List-II contains options showing how they depend on n.
Which of the following options has the correct combination considering List-I and List-II?
Which of the following options has the correct combination considering List-I and List-II?
A.
(III), (P)
B.
(III), (S)
C.
(IV), (U)
D.
(IV), (Q)
2019
Q193
JEE Advanced
MCQ
14 Mar 2026
Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the nth orbit of the atom and List-II contains options showing how they depend on n.
Which of the following options has the correct combination considering List-I and List-II?
Which of the following options has the correct combination considering List-I and List-II?
A.
(II), (R)
B.
(I), (P)
C.
(I), (T)
D.
(II), (Q)
2019
Q194
JEE Advanced
MSQ
14 Mar 2026
The ground state energy of hydrogen atom is $-$13.6 eV. Consider an electronic state $\psi $ of He+ whose energy, azimuthal quantum number and magnetic quantum number are $-$3.4 eV, 2 and 0, respectively.
Which of the following statement(s) is(are) true for the state $\psi $?
Which of the following statement(s) is(are) true for the state $\psi $?
A.
It is a 4d state
B.
The nuclear charge experienced by the electron in this state is less than 2e, where e is the magnitude of the electronic charge
C.
It has 2 angular nodes
D.
It has 3 radial nodes
2018
Q195
JEE Mains
MCQ
14 Mar 2026
Which of the following statements is false ?
A.
Photon has momentum as well as wavelength.
B.
Splitting of spectral lines in electrical field is called Stark effect.
C.
Rydberg constant has unit of energy.
D.
Frequency of emitted radiation from a black body goes from a lower wavelength to higher wavelength as the temperature increases.
2018
Q196
JEE Mains
MCQ
14 Mar 2026
The de-Broglie's wavelength of electron present in first Bohr orbit of 'H' atom is :
A.
0.529 $\mathop {\rm A}\limits^ \circ $
B.
2$\pi $ $ \times $ 0.529 $\mathop {\rm A}\limits^ \circ $
C.
${{0.529} \over {2\pi }}$ $\mathop {\rm A}\limits^ \circ $
D.
4 $ \times $ 0.529 $\mathop {\rm A}\limits^ \circ $
2018
Q197
JEE Mains
MCQ
14 Mar 2026
Ejection of the photoelectron from metal in the photoelectric experiment can be stopped by applying 0.5 V when the radiation of 250 nm is used. The work function of the metal is :
A.
4 eV
B.
4.5 eV
C.
5 eV
D.
5.5 eV
2017
Q198
JEE Mains
MCQ
14 Mar 2026
The electron in the hydrogen atom undergoes transition from higher orbitals
to orbital of radius 211.6 pm. This transition is associated with :
A.
Lyman series
B.
Balmer series
C.
Paschen series
D.
Brackett series
2017
Q199
JEE Mains
MCQ
14 Mar 2026
If the shortest wavelength in Lyman series of hydrogen atom is A, then the longest wavelength in Paschen series of He+ is :
A.
${{5A} \over 9}$
B.
${{9A} \over 5}$
C.
${{36A} \over 5}$
D.
${{36A} \over 7}$
2017
Q200
JEE Mains
MCQ
14 Mar 2026
The radius of the second Bohr orbit for hydrogen atom is:
(Planck’s Const. h = 6.6262 × 10-34 Js; mass of electron = 9.1091 × 10-31 kg; charge of electron (e) = 1.60210 × 10-19 C; permittivity of vacuum (${\varepsilon _0}$) = 8.854185 × 10-12 kg-1 m-3 A2)
(Planck’s Const. h = 6.6262 × 10-34 Js; mass of electron = 9.1091 × 10-31 kg; charge of electron (e) = 1.60210 × 10-19 C; permittivity of vacuum (${\varepsilon _0}$) = 8.854185 × 10-12 kg-1 m-3 A2)
A.
4.76 $\mathop {\rm A}\limits^o $
B.
2.12 $\mathop {\rm A}\limits^o $
C.
0.529 $\mathop {\rm A}\limits^o $
D.
1.65 $\mathop {\rm A}\limits^o $