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The sum of the degenerate orbitals of $ 2^{\text{nd}} $ excited state for $ \mathrm{He^{+}} $ ion and $ \mathrm{He} $ atom is ______.

Consider the following spectral lines for atomic hydrogen:
A. First line of Paschen series
B. Second line of Balmer series
C. Third line of Paschen series
D. Fourth line of Bracket series
The correct arrangement of the above lines in ascending order of energy is:

If shortest wavelength of hydrogen atom in Lyman series is \$ x \$, then longest wavelength in Balmer series of \$ \\mathrm{He^+} \$ is:

The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is __________ $ \text{J mol}^{-1} $. Given: $ R_H = 2.18 \times 10^{-11} \, \text{ergs} $.

Given,
(A) $n = 5, m_{\ell} = -1$
(B) $n = 3, \ell = 2, m_{\ell} = -1, m_s = +\frac{1}{2}$
The maximum number of electron(s) in an atom that can have the quantum numbers as given in (A) and (B) respectively are:

Arrange the following atomic orbitals of multi electron atoms in order of increasing energy.
A. $ n = 3, \, l = 2, \, m = +1 $
B. $ n = 4, \, l = 0, \, m = 0 $
C. $ n = 6, \, l = 1, \, m = 0 $
D. $ n = 5, \, l = 1, \, m = +1 $
E. $ n = 2, \, l = 1, \, m = +1 $
Choose the correct answer from the options given below:

Given below are two statements:
Statement I : When an electric discharge is passed through gaseous hydrogen, the hydrogen molecules dissociate and the energetically excited hydrogen atoms produce electromagnetic radiation of discrete frequencies.
Statement II : The frequency of second line of Balmer series obtained from $ \mathrm{He^+} $ is equal to that of first line of Lyman series obtained from hydrogen atom.
In the light of the above statements, choose the correct answer from the options given below:

The surface of sodium metal is irradiated with radiation of wavelength $ x \, \text{nm} $. The kinetic energy of ejected electrons is $ 2.8 \times 10^{-20} \, \text{J} $. The work function of sodium is $ 2.3 \, \text{eV} $. The value of $ x $ is ______ $ \times 10^{2} \, \text{nm} $. (Nearest integer)

(Given : $ 6.6 \times 10^{-34} \, \text{J s} $; $ 1e = 1.6 \times 10^{-19} \, \text{J} $; $ c = 3.0 \times 10^{8} \, \text{m s}^{-1} $ )

Identify the INCORRECT statements from the following:
A. Notation $ ^{24}_{12}\mathrm{Mg} $ represents $ 24 $ protons and $ 12 $ neutrons.
B. Wavelength of a radiation of frequency $ 4.5 \times 10^{15} \, \text{s}^{-1} $ is $ 6.7 \times 10^{-8} \, \text{m} $.
C. One radiation has wavelength $ \lambda_1 = 900 \, \text{nm} $ and energy $ = E_1 $; other radiation has wavelength = $ \lambda_2 (300 \, \text{nm}) $ and energy $ = E_2 $. $ E_1 : E_2 = 3 : 1 $.
D. Number of photons of light of wavelength $ 2000 \, \text{pm} $ that provides $ 1 \, \text{J} $ of energy is $ 1.006 \times 10^{16} $.
Choose the correct answer from the options given below:

10.

What is the ratio of wave number of first line (lowest energy line) of Balmer series of $ \text{H} $ atomic spectrum to first line of its Brackett series?

11.

The wavelength of spectral line obtained in the spectrum of $ \mathrm{Li^{2+}} $ ion, when the transition takes place between two levels whose sum is $ 4 $ and difference is $ 2 $, is:

12.

Identify the correct statements from the following:
A. Heisenberg uncertainty principle is applicable to electrons.
B. The size of $ 2p_{x} $ orbital is less than the size of $ 3p_{x} $ orbital.
C. The energy of $ 2s $ orbital of H atom is equal to the energy of $ 2s $ orbital of Li.
D. The electronic configuration of Cr is $ [\mathrm{Ar}] \, 3d^{5} \, 4s^{1} $
Choose the correct answer from the options given below:

13.

The hydrogen spectrum consists of several spectral lines in Lyman series $ (L_1, L_2, L_3, \ldots; \, L_1 $ has lowest energy among Lyman series). Similarly it consists of several spectral lines in Balmer series $ (B_1, B_2, B_3, \ldots; \, B_1 $ has lowest energy among Balmer lines). The energy of $ L_1 $ is $ x $ times the energy of $ B_1 $. The value of $ x $ is _______ $ \times 10^{-1} $. (Nearest integer)

14.

The spin only magnetic moment of $ \mathrm{Cu^+} $ ion is: [Given: Atomic number of copper ($ \mathrm{Cu} $) $ = 29 $]

15.

When a certain metal was irradiated with light of frequency $ 4.0 \times 10^{16} \, \text{s}^{-1} $, the photoelectrons emitted has three times the kinetic energy as the kinetic energy of photoelectrons emitted when the metal was irradiated with light of frequency $ 2.0 \times 10^{16} \, \text{s}^{-1} $. The threshold frequency $ (v_0 $) of the metal is:

16.

Consider two radiations of wavelength.
$1$. $\lambda_1=2000\mathring A$ $2$. $\lambda_2=6000 \mathring A$
The ratio of the energies of these two radiations $ \left( \dfrac{E_1}{E_2} \right) $ is ______. (Nearest integer)

17.

What is the energy (in $ \text{J atom}^{-1} $) required for the following process?
$ \mathrm{Li^{2+}(g)} \rightarrow \mathrm{Li^{3+}(g)} + e^{-} $
(Take the ionization energy for the H atom in the ground state as $ 2.18 \times 10^{-18} \, \text{J atom}^{-1} $)

18.

The figure shows a sample of $ \mathrm{H} $-atoms having electron revolving in higher orbit ‘$ n $’.

If this electron makes transition from this orbit ‘$ n $’ to ground state, number of lines emitted in Balmer series are:

19.

Consider a hydrogen like ion with an unknown atomic number $ Z $. An electron transition from the $ n = 3 $ state to the $ n = 2 $ state, emitting a photon of wavelength $ 70 \, \text{nm} $. If the same transition in a hydrogen atom ($ Z = 1 $) occurs with the emission of a photon with a wavelength of $ 630 \, \text{nm} $. The value of $ Z $ and the ion is:

20.

Q. 53
Match the List-I with List-II.

List-I Orbital	List-II Radial nodes and nodal Plane
A. \$ 2s \$	II. \$ 1 \$ Radial node + Two nodal planes
B. \$ 3s \$	I. \$ 1 \$ Radial node + One nodal plane
C. \$ 3p \$	III. \$ 2 \$ Radial nodes + No nodal plane
D. \$ 4d \$	IV. \$ 1 \$ Radial node + No nodal plane

Choose the correct answer from the option given below:

21.

The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series.

(R = Rydberg constant)

22.

The species having identical radii according to the Bohr's theory are:
A. H (first orbit) B. $ \mathrm{He^{+}} $ (first orbit)
C. $ \mathrm{He^{+}} $ (Second orbit) D. $ \mathrm{Li^{2+}} $ (first orbit)
E. $ \mathrm{Be^{3+}} $ (Second orbit)
Choose the correct answer from the options given below:

23.

The energy of first (lowest) Balmer line of $ \mathrm{H} $ atom is $ x \, \text{J} $. The energy (in $ \text{J} $) of second Balmer line of $ \mathrm{H} $ atom is:

24.

Which of the following is correct set of $ 4 $ quantum numbers of $ 19^{\\text{th}} $ electron in Chromium (Atomic number $ = 24 $) in accordance with Aufbau principle?

25.

Figure $ 1 $. Electron parabability density for $ 2s $ orbital

Figure $ 2 $. wave function for $ 2s $ orbital
Which of the following point in Figure $ 2 $ most accurately represents the nodal surface as shown in Figure $ 1 $?

26.

Three particle $ A $, $ B $ and $ C $ have masses $ m $, $ 2m $ and $ 4m $ while their kinetic energies are $ 2K $, $ 4K $ and $ K $ respectively. If $ \lambda_A $, $ \lambda_B $ and $ \lambda_C $ denote their de Broglie wavelengths, then:

27.

The Bohr radius of a hydrogen like species is $ 70.53 \, \text{pm} $. The species and the stationary state $ (n) $ are respectively.
(Given: Hydrogen atom Bohr radius is $ 52.9 \, \text{pm} $)

28.

The work functions of two metals ($ M_A $ and $ M_B )$ are in the $ 1:2 $ ratio. When these metals are exposed to photons of energy $ 6 \, \text{eV} $, the kinetic energy of liberated electrons of $ M_A : M_B $ is in the ratio of $ 2.642 : 1 $. The work function (in eV) of $ M_A $ and $ M_B $ are respectively,

29.

Which of the following statement(s) is/are true?
A. If two orbitals have the same value of $ (n + l) $, the orbital with lower value of $ n $ will have lower energy.
B. Energies of the orbitals in the same subshell increase with increase in atomic number.
C. The size of $ 2p_{x} $ orbital is less than the size of $ 3p_{x} $ orbital.
D. Among $ 5f, 6s, 4d, 5p $ and $ 5d $ orbitals, none of the orbitals have $ 2 $ radial nodes.
Choose the correct answer from the options given below:

30.

First and second ionization enthalpies of lithium are $ 520 \, \text{kJ} \, \text{mol}^{-1} $ and $ 7297 \, \text{kJ} \, \text{mol}^{-1} $ respectively. Energy required to convert $ 3.5 \, \text{mg} $ lithium (g) into $ \text{Li}^{2+}(g) $ [$ \text{Li}(g) \rightarrow \text{Li}^{2+}(g) $] is ________ $ \text{kJ} \, \text{mol}^{-1} $. (Nearest integer)
[Molar mass of Li = $ 7 \, \text{g} \, \text{mol}^{-1} $]

31.

Which of the following statements regarding the energy of the stationary state is true in the following one-electron systems?

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JEE Main 2026 6th April Morning Shift

If shortest wavelength of hydrogen atom in Lyman series is \$ x \$, then longest wavelength in Balmer series of \$ \\mathrm{He^+} \$ is:

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