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]

Related Formula

Core Logic

Statement I is a verbatim definition of Heisenberg's Uncertainty Principle, hence it is completely true.

For Statement II, we are given that Delta x = Delta p$Delta x = Delta p$:

Since Delta p = m cdot Delta v$Delta p = m cdot Delta v$:

This perfectly matches Statement II, so it is also true.

Pattern Recognition

When solving inequality bounds for identical uncertainties, always substitute directly to obtain a clean quadratic form before taking the square root.

Chapter Mix

Class 11 Chemistry: Structure of Atom

Core Logic

In multi-electron systems, the energy profile depends on both the primary shell (n$n$) and azimuthal subshell (l$l$) quantum values via the (n+l)$(n+l)$ rule. Orbitals sharing the exact same n$n$ and l$l$ values are energy-degenerate as long as external field metrics are zero. Let us map each set:

• A: 1s$1s$
• B: 2s$2s$
• C: 2p$2p$
• D: 3d$3d$ (ml = 1$m_l = 1$)
• E: 3d$3d$ (ml = 0$m_l = 0$)

Since both D and E describe subcomponents of the same 3d$3d$ subshell (n=3, l=2$n=3, l=2$), they share identical energies, establishing perfect degeneracy.

Pattern Recognition

Sees: Orbitals matching energy level in multi-electron space. Trap: Confusing single-electron hydrogen atoms (where energy depends solely on n$n$) with multielectron atoms.

Chapter Mix

Class 11 Chemistry: Structure of Atom

Related Formula

Core Logic

The ground-state electronic configuration of Chromium (Z=24$Z=24$) is anomalous due to half-filled stability:

Now count the electrons in specific subshells:

• For l = 1$l = 1$ (p-electrons): present in 2p⁶$2p^6$ and 3p⁶ 6 + 6 = 12$3p^6 \implies 6 + 6 = 12$ electrons.
• For l = 2$l = 2$ (d-electrons): present in 3d⁵ 5$3d^5 \implies 5$ electrons.

Thus, the counts are 12 and 5 respectively.

Pattern Recognition

Always remember the 3d⁵ 4s¹$3d^5 4s^1$ exception for Chromium (Z=24$Z=24$) and 3d¹⁰ 4s¹$3d^{10} 4s^1$ for Copper (Z=29$Z=29$). Forgetting the half-filled d-subshell exception will lead to the wrong answer (12 and 4).

Chapter Mix

Class 11 Chemistry: Structure of Atom

Core Logic

Let's evaluate each statement using quantum mechanics:

• Statement (1) is correct: The wave function squared Ψ²$\Psi^2$ (probability density) for a 1s orbital peaks directly at the nucleus (r = 0$r = 0$).
• Statement (2) is correct: The boundary distribution curves drop off exponentially but approach zero only at infinity, meaning the electron has a non-zero probability of being found at any distance, including 2a₀$2a_0$.
• Statement (3) is correct: All s-orbitals have an angular wave function component of unity, making them perfectly spherical.
• Statement (4) is incorrect: The total energy of a bound electron in a hydrogen atom is constant for a given principal quantum number quantum state (E = -13.6~eV$E = -13.6\mathrm{~eV}$ when n=1$n=1$), independent of its spatial distance from the nucleus.

Pattern Recognition

Total energy is a fixed state property defined strictly by the principal quantum number n$n$. It never varies as a function of the electron's position coordinates within that orbital state.

Chapter Mix

Class 11 Chemistry: Structure of Atom