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