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Number of spectral lines obtained in \( \mathrm{He^+} \) spectra, when an electron makes transition form fifth excited state to first excited state will be:

The value of Rydberg constant \( (R_H) \) is \( 2.18 \times 10^{-18} \, \text{J} \). The velocity of electron having mass \( 9.1 \times 10^{-31} \, \text{kg} \) in Bohr’s first orbit of hydrogen atom = __________ \( \times 10^{5} \) \( \text{ms}^{-1} \) (nearest integer).

The total number of anti bonding molecular orbitals, formed from \( 2s \) and \( 2p \) atomic orbitals in a diatomic molecule is __________.

Frequency of the de-Broglie wave of electron in Bohr’s first orbit of hydrogen atom is __________ \( \times 10^{13} \) \( \mathrm{Hz} \) (nearest integer).
[Given: \( R_H \) (Rydberg constant) \( = 2.18 \times 10^{-18} \ \mathrm{J} \), \( h \) (Plank’s constant) \( = 6.6 \times 10^{-34} \ \mathrm{J\cdot s} \).]

Match List I with List II.

LIST I (Spectral Series for Hydrogen)	LIST II (Spectral Region/Higher Energy State)
A. Lyman	I. Infrared region
B. Balmer	II. UV region
C. Paschen	III. Infrared region
D. Pfund	IV. Visible region

Choose the correct answer from the options given below:

The number of radial node/s for \( 3p \) orbital is:

According to the wave-particle duality of matter by de-Broglie, which of the following graph plot presents most appropriate relationship between wavelength of electron \( \lambda \) and momentum of electron \( p \)?

Which of the following electronic configuration would be associated with the highest magnetic moment ?

Based on Heisenberg’s uncertainty principle, the uncertainty in the velocity of the electron to the found within an atomic nucleus of diameter \( 10^{-15} \, \text{m} \) is _____ \( \times 10^{9} \, \text{ms}^{-1} \) (nearest integer)
[Given : mass of electron \( = 9.1 \times 10^{-31} \, \text{kg} \). Plank's constant \( (h) = 6.626 \times 10^{-34} \, \text{Js} \)] (Value of \( \pi = 3.14 \))

10.

The de-Broglie’s wavelength of an electron in the \( 4^{\text{th}} \) orbit is \( \_\_\_\_\_\_ \, \pi a_0 \). \( (a_0 = \) Bohr’s radius\() \)

11.

Given below are two statements:
Statement (I): The orbitals having same energy are called as degenerate orbitals.
Statement (II): In hydrogen atom, \( 3p \) and \( 3d \) orbitals are not degenerate orbitals.
In the light of the above statements, choose the most appropriate answer from the options given below:

12.

The number of electrons present in all the completely filled subshells having \( n = 4 \) and \( s = +\frac{1}{2} \) is __________. (Where \( n \) = principal quantum number and \( s \) = spin quantum number)

13.

The maximum number of orbitals which can be identified with \( n = 4 \) and \( m_{1} = 0 \) is ____________ .

14.

Choose the incorrect statement about Dalton’s Atomic Theory:

15.

The ionization energy of sodium in \( \text{kJ mol}^{-1} \), if electromagnetic radiation of wavelength \( 242 \, \text{nm} \) is just sufficient to ionize sodium atom is ______.

16.

Wave number for a radiation having \( 5800 \mathring{\text{A}} \) wavelength is \( x \times 10 \, \text{cm}^{-1} \). The value of \( x \) is ____________.(Integer answer)

17.

For hydrogen atom energy of an electron in first excited state is \( -3.4 \, \text{eV} \), K.E. of the same electron of hydrogen atom is \( x \, \text{eV} \). Value of \( x \) is __________ \( \times 10^{-1} \, \text{eV} \) (Nearest integer)

18.

Compare the energies of following sets of quantum numbers for multielectron system.

(A) \( n = 4, \, l = 1 \) (B) \( n = 4, \, l = 2 \) (C) \( n = 3, \, l = 1 \)

(D) \( n = 3, \, l = 2 \) (E) \( n = 4, \, l = 0 \)

Choose the correct answer from the options given below:

19.

The four quantum numbers for the electron in the outer most orbital of potassium (atomic no. \( 19 \)) are:

20.

In an atom, total number of electrons having quantum numbers \( n = 4 \), \( |m_\ell| = 1 \) and \( m_s = -\dfrac{1}{2} \) is \( \_ \_ \_ \_ \_ \).

21.

A hypothetical electromagnetic wave is show below:

The frequency of the wave is \( x \times 10^{19} \) Hz, \( x = \) ______ (Nearest integer)

22.

The correct set of four quantum numbers for the valence electron of rubidium atom \( (Z = 37) \) is:

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JEE Main 2024 31st Jan Evening Shift

The four quantum numbers for the electron in the outer most orbital of potassium (atomic no. \( 19 \)) are:

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