Question

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.

  

• B.

  

• C.

  

• D.

  

Hint:

The energy of a hydrogen-like atom is proportional to \( Z^2 \), so the plot of \( E \) versus \( Z \) should show a parabolic increase.

Answer 1

The Correct Option is B

Option B: A graph of energy \( E \) versus atomic number \( Z \) for a hydrogen-like species. The energy levels in hydrogen-like atoms are defined by the formula:

\( E_n = - \frac{13.6 \, \text{eV}}{n^2} \times Z^2 \)

Definitions:

• \( E_n \): Energy of the stationary state (in electron volts).
• \( Z \): Atomic number.
• \( n \): Principal quantum number.

This graph would illustrate energy \( E \) decreasing as \( Z \) increases, owing to the \( Z^2 \) dependency. Consequently, the graph should depict a downward trend as \( Z \) rises.

Should you require further clarification or an alternative graph representation, please inquire!