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JEE MainChemistryStructure of Atom

For a hydrogen-like species with a constant atomic number, which of the following best describes the shape of the plot of total energy ( E ) versus principal quantum number ( n )?

Options

  1. AA downward-opening parabola in the fourth quadrant starting from the origin
  2. BA straight line in the fourth quadrant with a negative slope
  3. CA curve in the first quadrant that asymptotically approaches the x-axis from above
  4. DA curve in the fourth quadrant that asymptotically approaches the x-axis from below

Correct answer

D. A curve in the fourth quadrant that asymptotically approaches the x-axis from below

Step-by-step solution

The total energy of an electron in the n^ th orbit of a hydrogen-like species is given by: E_n = -13.6 Z^2 n^2 eV For a constant atomic number Z , E_n - 1 n^2 . Since n is a positive integer, E_n is always negative. As n increases, the magnitude of E_n decreases, meaning it becomes less negative and approaches zero. Graphically, this corresponds to a curve in the fourth quadrant (where energy is negative) that asymptotically approaches the x -axis ( E=0 ) from below. Answer: A curve in the fourth quadrant that asym

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