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

Which of the following elements has a half-filled valence shell?

The ground state energy of a 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 $\Psi$?
$(1)$ It has $2$ angular nodes
$(2)$ It has $3$ radial nodes
$(3)$ It is a $4d$ state
$(4)$ The nuclear charge experienced by the electron in this state is less than $2e$,where $e$ is the magnitude of the electronic charge.

Match List-$I$ with List-$II$ :

List-$I$ (Quantum number)	List-$II$ (Orbital)
$a. n=2, \ell=1$	$i. 2s$
$b. n=3, \ell=2$	$ii. 3s$
$c. n=3, \ell=0$	$iii. 2p$
$d. n=2, \ell=0$	$iv. 3d$

Choose the correct answer from the options given below :

What is the relationship between the shapes of $3d_{xy}$ and $3d_{x^2-y^2}$ orbitals?

The extra stability of half-filled subshells 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
Identify the correct statements.