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 for the energy \( E \) versus the atomic number \( Z \) for a hydrogen-like species. In hydrogen-like atoms, the energy levels are given by the formula:

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

where:

• \( E_n \) is the energy of the stationary state (in electron volts),
• \( Z \) is the atomic number,
• \( n \) is the principal quantum number.

The graph you are asking about would show a curve where energy \( E \) decreases as \( Z \) increases, due to the \( Z^2 \) dependence of the energy on the atomic number. Therefore, the graph should show a downward curve as \( Z \) increases.

If you need any further explanation or a different representation of the graph, feel free to ask!