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

Related Formula

Core Logic

For a constant principal quantum number n$n$, the energy E$E$ is directly proportional to -Z²$-Z^2$. This represents a quadratic relation where the curve is a downward-opening parabola starting from the origin in the negative energy region.

Pattern Recognition

Since energy values are inherently negative for bound states, as Z$Z$ increases, E$E$ becomes rapidly more negative following a parabolic curve.

Chapter Mix

Class 11 Chemistry: Structure of Atom

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