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Correct statements for an element with atomic number \( 9 \) are:
A. There can be \( 5 \) electrons for which \( m_s = +\frac{1}{2} \) and \( 4 \) electrons for which \( m_s = -\frac{1}{2} \).
B. There is only one electron in \( p_z \) orbital.
C. The last electron goes to orbital with \( n = 2 \) and \( l = 1 \).
D. The sum of angular nodes of all the atomic orbitals is \( 1 \).
Choose the correct answer from the options given below:

Radius of the first excited state of Helium ion is given as:
\( a_0 \to \) radius of first stationary state of hydrogen atom.

For hydrogen like species, which of the following graphs provides the most appropriate representation of \( E \) vs \( Z \) plot for a constant \( n \)?
[\( E \): Energy of the stationary state,
\( Z \): atomic number, \( n \) = principal quantum number]

In a multielectron atom, which of the following orbitals described by three quantum numbers will have same energy in absence of electric and magnetic fields?
A. \( n = 1, \, \ell = 0, \, m_1 = 0 \) B. \( n = 2, \, \ell = 0, \, m_1 = 0 \)
C. \( n = 2, \, \ell = 1, \, m_1 = 1 \) D. \( n = 3, \, \ell = 2, \, m_1 = 1 \)
E. \( n = 3, \, \ell = 2, \, m_1 = 0 \)
Choose the correct answer from the options given below:

Given below are two statements:
Statement (I): For a given shell, the total number of allowed orbitals is given by \( n^2 \).
Statement (II): For any subshell, the spatial orientation of the orbitals is given by \( -l \) to \( +l \) values including zero.
In the light of the above statements, choose the correct answer from the options given below:

Which of the following statements are true?
(A) The subsidiary quantum number \( l \) describes the shape of the orbital occupied by the electron.
(B) is the boundary surface diagram of the \( 2p_x \) orbital.
(C) The \( + \) and \( - \) signs in the wave function of the \( 2p_x \) orbital refer to charge.
(D) The wave function of \( 2p_x \) orbital is zero everywhere in the \( xy \) plane.
Choose the correct answer from the options given below:

According to Bohr model of hydrogen atom, which of the following statement is incorrect?

Given below are two statements about X-ray spectra of elements:
Statement (I): A plot of \( \sqrt{\nu} \) (\( \nu = \) frequency of X-rays emitted) vs atomic mass is a straight line.
Statement (II): A plot of \( \nu \) (\( \nu = \) frequency of X-rays emitted) vs atomic number is a straight line.
In the light of the above statements, choose the correct answer from the options given below:

For electrons in ‘\( 2s \)’ and ‘\( 2p \)’ orbitals, the orbital angular momentum values, respectively are:

For hydrogen atom, the orbital/s with lowest energy is/are:
(A) \( 4s \) (B) \( 3p_x \) (C) \( 3d_{x^2-y^2} \) (D) \( 3d_{z^2} \) (E) \( 4p_z \)
Choose the correct answer from the options given below:

If $a_0$ is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength ($\lambda$) of the electron present in the second orbit of hydrogen atom? [$n$ : any integer]

Which one of the following about an electron occupying the \( 1\text{s} \) orbital in a hydrogen atom is incorrect? \( \text{(Bohr’s radius is represented by } a_0 \text{)} \)

Which of the following statements are correct, if the threshold frequency of caesium is \( 5.16 \times 10^{14} \, \mathrm{Hz} \)?
A. When \( \mathrm{Cs} \) is placed inside a vacuum chamber with an ammeter connected to it and yellow light is focused on \( \mathrm{Cs} \), the ammeter shows the presence of current
B. When the brightness of the yellow light is dimmed, the value of the current in the ammeter is reduced
C. When a red light is used instead of the yellow light, the current produced is higher with respect to the yellow light
D. When a blue light is used, the ammeter shows the formation of current
E. when a white light is used, the ammeter shows formation of current
Choose the correct answer from the options given below:

The correct stability order of the following species/molecules is:

Which of the following is/are not correct with respect to energy of atomic orbitals of hydrogen atom?
(A) \( 1s < 2p < 3d < 4s \) (B) \( 1s < 2s = 2p < 3s = 3p \)
(C) \( 1s < 2s < 2p < 3s < 3p \) (D) \( 1s < 2s < 4s < 3d \)
Choose the correct answer from the options given below:

Given below are two statements:
Statement (I): It is impossible to specify simultaneously with arbitrary precision, both the linear momentum and the position of a particle.
Statement (II): If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron, then the uncertainty in the measurement of velocity is \(\displaystyle \ge \sqrt{\frac{h}{\pi}} \times \frac{1}{2m} \).
In the light of the above statements, choose the correct answer from the options given below:

The extra stability of half-filled subshell is due to:
(A) Symmetrical distribution of electrons
(B) Smaller coulombic repulsion energy
(C) The presence of electrons with the same spin in non-degenerate orbitals
(D) Larger exchange energy
(E) Relatively smaller shielding of electrons by one another
Indentify the correct statements;

Given below are two statements:
Statement (I) : A spectral line will be observed for a \( 2p_x \to 2p_y \) transition.
Statement (II) : \( 2p_x \) and \( 2p_y \) (are degenerate orbitals.
In the light of the above statements, choose the correct answer from the options given below:

Consider the ground state of chromium atom (\( Z = 24 \)). How many electrons are with Azimuthal quantum number \( l = 1 \) and \( l = 2 \) respectively?

Which of the following postulate of Bohr’s model of hydrogen atom is not in agreement with quantum mechanical model of an atom?

The energy of an electron in first Bohr orbit of H-atom is \( -13.6 \, \text{eV} \). The magnitude of energy value of electron in the first excited state of \( \mathrm{Be}^{3+} \) is ______ eV. (Nearest integer value)

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JEE Main 2025 29th Jan Morning Shift

If $a_0$ is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength ($\lambda$) of the electron present in the second orbit of hydrogen atom? [$n$ : any integer]