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

Solution & Explanation

### Related Formula According to the quantum mechanical model, the position and momentum of an electron cannot be determined simultaneously with absolute certainty as per Heisenberg's Uncertainty Principle: Delta x cdot Delta p ge frach4pi ### Core Logic Bohr's model defines fixed circular orbits for electrons around the nucleus, implying precise knowledge of both trajectory and position. However, the quantum mechanical model replaces these deterministic circular paths with three-dimensional probability distributions known as orbitals, where the path is spherical for the ground state of hydrogen. ### Step 1: Evaluation of Options Postulates (1), (2), and (3) regarding discrete energy levels, stationary states, and photon emissions are preserved in the quantum mechanical framework. Postulate (4) incorrectly confines the electron to a defined circular two-dimensional path, which directly contradicts quantum mechanical principles. ### Pattern Recognition Sees: "Bohr's model not in agreement with Quantum Mechanics" ightarrow Look for deterministic trajectories like "moves in a circle" or "fixed path". Quantum mechanics is probabilistic, not deterministic. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Structure of Atom

Reference Study Guides

Structure Of Atom

More Structure of Atom Previous-Year Questions — Page 2

Q47 2025 Bohr's Model
The energy of an electron in the first Bohr orbit of the Hydrogen atom is -13.6 text eV. The magnitude of the energy value of an electron in the first excited state of the textBe^3+ ion is _________ eV (as the nearest integer value).
Numerical Answer. Answer: 54 to 54

Solution

### Related Formula Bohr energy level formula for hydrogenic species: E_n = -13.6 times fracZ^2n^2 quad texteV where: Z = atomic number of the species n = principal quantum number of the orbit ### Execution Step 1: Identify the parameters for the first excited state of textBe^3+: * For Beryllium (textBe), the atomic number is Z = 4. * The term 'first excited state' refers to the second energy level, so n = 2. Step 2: Substitute these values into the Bohr energy equation: E_textBe^3+ = -13.6 times frac4^22^2 = -13.6 times frac164 E_textBe^3+ = -13.6 times 4 = -54.4 text eV Step 3: Extract the magnitude and round to the nearest integer value: |E_textBe^3+| = 54.4 approx 54 ### Pattern Recognition For the first excited state of Beryllium (Z=4, n=2), the term fracZ^2n^2 = frac4^22^2 = frac164 = 4. Thus, the energy value is exactly 4 times that of the ground-state hydrogen atom (13.6 times 4 = 54.4). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Structure of Atom
Q27 2025 Bohr Model for Hydrogen-like Species
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]
  • A. Graph (1)
  • B. Graph (2)
  • C. Graph (3)
  • D. Graph (4)

Solution

### Related Formula E_n = -13.6 fracZ^2n^2text eV ### Core Logic For a constant principal quantum number n, the energy E is directly proportional to -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 increases, E becomes rapidly more negative following a parabolic curve. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Structure of Atom
Q40 2025 Heisenberg's Uncertainty Principle
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 gesqrtfrachpitimesfrac12m In the light of the above statements, choose the correct answer from the options given below:
  • A. Statement I is true but Statement II is false.
  • B. Both Statement I and Statement II are true.
  • C. Statement I is false but Statement II is true.
  • D. Both Statement I and Statement II are false.

Solution

### Related Formula Delta x cdot Delta p ge frach4pi ### 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 p cdot Delta p ge frach4pi implies (Delta p)^2 ge frach4pi Delta p ge sqrtfrach4pi = frac12sqrtfrachpi Since Delta p = m cdot Delta v: m cdot Delta v ge frac12sqrtfrachpi implies Delta v ge frac12msqrtfrachpi 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. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Structure of Atom
Q38 2025 Quantum Numbers and Orbital Energies
In a multielectron atom, which of the following orbitals described by three quantum numbers with have same energy in absence of electric and magnetic fields? A. n = 1, l = 0, m_l = 0 B. n = 2, l = 0, m_l = 0 C. n = 2, l = 1, m_l = 1 D. n = 3, l = 2, m_l = 1 E. n = 3, l = 2, m_l = 0 Choose the correct answer from the options given below:
  • A. textA and B only
  • B. textB and C only
  • C. textC and D only
  • D. textD and E only

Solution

### Core Logic In multi-electron systems, the energy profile depends on both the primary shell (n) and azimuthal subshell (l) quantum values via the (n+l) rule. Orbitals sharing the exact same n and l values are energy-degenerate as long as external field metrics are zero. Let us map each set: - **A:** 1s - **B:** 2s - **C:** 2p - **D:** 3d (m_l = 1) - **E:** 3d (m_l = 0) Since both D and E describe subcomponents of the same 3d subshell (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) with multielectron atoms. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Structure of Atom

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