Question

Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Z are defined by their principal quantum number n, where n >> Z. Which of the following statement(s) is (are) true?

I. The energy of these states approaches zero as n approaches infinity.
II. The electron density is concentrated near the nucleus.
III. These states have longer lifetimes compared to lower energy states.
a) I only
b) II only
c) I and III
d) I, II, and III

Answer 1

The truthfulness of statements regarding Rydberg states of hydrogen-like atoms can't be determined without seeing the statements. However, the energy states are quantized according to the Bohr model, with energy En = Z²E0/n², where n is the principal quantum number.

Step-by-step explanation:

The question you've asked pertains to the energy states of hydrogen-like atoms in highly excited states, also known as Rydberg states. The energy states of hydrogen and hydrogen-like atoms are described by the Bohr model, which quantizes these states according to certain rules governed by the principal quantum number n.

According to Bohr's formula for the energies of electron states in hydrogen-like atoms, the energy En can be expressed as Z²E0/n², where Z is the nuclear charge and E0 is the energy of the most tightly bound state (ground state). Hence, as the principal quantum number n increases, indicating highly excited states, the energy of the state relative to the ground state becomes smaller and the electron orbitals become larger.

To address your specific question about the truth of certain statements about Rydberg states, we would need to see the list of statements (I, II, and III) you provided before we can determine their truthfulness. Nonetheless, the information on quantum states and the Bohr model should help elucidate the behavior of electrons in highly excited or Rydberg states.