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

Solution & Explanation

### Related Formula textAzimuthal Quantum Number: l=1 implies textp-orbital, quad l=2 implies textd-orbital ### Core Logic The ground-state electronic configuration of Chromium (Z=24) is anomalous due to half-filled stability: Cr: 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^5 \, 4s^1 Now count the electrons in specific subshells: - For l = 1 (p-electrons): present in 2p^6 and 3p^6 implies 6 + 6 = 12 electrons. - For l = 2 (d-electrons): present in 3d^5 implies 5 electrons. Thus, the counts are **12 and 5** respectively. ### Pattern Recognition Always remember the 3d^5 4s^1 exception for Chromium (Z=24) and 3d^10 4s^1 for Copper (Z=29). Forgetting the half-filled d-subshell exception will lead to the wrong answer (12 and 4). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Structure of Atom

Reference Study Guides

More Structure of Atom Previous-Year Questions — Page 4

Q40 2025 Bohr's Model and de-Broglie Wavelength
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]
  • A. frac2mathrma_0mathrmnpi
  • B. frac8pi a_0n
  • C. frac4 pi a0n
  • D. frac4mathrmnpimathrma0

Solution

### Related Formula 2pi r_n = nlambda r_n = a_0 cdot n^2 ### Core Logic According to Bohr's quantization postulate condition coupled with de-Broglie's hypothesis : 2pi r_n = nlambda For the second orbit (n = 2), the radius is: r_2 = a_0 cdot (2)^2 = 4a_0 Substituting into the wave perimeter formula : 2pi (4a_0) = nlambda lambda = frac8pi a_0n This strictly matches option (2). ### Pattern Recognition The circumference of an electron's orbit must encompass an exact integral count of complete standing de-Broglie wave wavelengths. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Structure of Atom

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