Consider the following portion of the energy-level diagram for hydrogen:
-On a planet where the temperature is so high, the ground state of an electron in the hydrogen atom is n = 4. What is the ratio of IE on this planet to that on earth?
A) 1:16
B) 1:4
C) 4:1
D) 16:1
E) 1:1

Question

Consider the following portion of the energy-level diagram for hydrogen: 
-On a planet where the temperature is so high, the ground state of an electron in the hydrogen atom is n = 4. What is the ratio of IE on this planet to that on earth?
A) 1:16 
B) 1:4 
C) 4:1 
D) 16:1 
E) 1:1

Quizplus · Accepted Answer

The ionization energy (IE) of a hydrogen atom is inversely proportional to the square of the principal quantum number n (IE ∝ 1/n^2). On Earth, the ground state of hydrogen is n = 1, and on this hypothetical planet, it is n = 4. Therefore, the ratio of ionization energies is (1/1^2) : (1/4^2) = 1 : 1/16, which simplifies to 16:1. However, the question asks for the ratio on the planet to that on Earth, so the correct ratio is the inverse, 1:16.

Consider the Following Portion of the Energy-Level Diagram for Hydrogen