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JEE MainChemistryStructure of Atom

For a hydrogen-like ion, the radial wave function of the 2 s orbital is proportional to (2 - Zr a₀ ) e^ -Zr/2a₀ , where Z is the atomic number and a₀ is the Bohr radius. If a radial node for this orbital is observed at a distance of r = 0.5 a₀ from the nucleus, the hydrogen-like ion is

Options

  1. ABe ³⁺
  2. BHe ⁺
  3. CH
  4. DLi ²⁺

Correct answer

A. Be ³⁺

Step-by-step solution

A radial node is a region where the probability of finding an electron is zero, meaning the radial wave function must be zero. Setting the polynomial part of the given wave function to zero: 2 - Zr a₀ = 0 Solving for the position of the node r : Zr a₀ = 2 r = 2a₀ Z It is given that the radial node is observed at r = 0.5 a₀ . Equating the theoretical position to the given value: 2a₀ Z = 0.5 a₀ Solving for the atomic number Z : Z = 2 0.5 = 4 The atomic number Z = 4 corresponds to Beryllium. Therefore, the hydrogen-li

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