Question

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 ionization energy (IE) on this planet to that on earth?

Answer 1

Answer:

1:16

Explanation:

The ground state of an electron on the planet is n = 4 compared the ground state of an electron at n =1. For a hydrogen atom, the electron energy level is given as:

$E(n)=\frac{13.6}{n^2}\\ \\Where\ n\ is\ the\ ionization \ energy$

$E(4)=\frac{13.6}{4^2}=\frac{13.6}{16}\\ \\E(1)=\frac{13.6}{1^2}=\frac{13.6}{1}\\ \\The\ ratio\ of\ their\ ionization\ energy=\frac{E(4)}{E(1)} =\frac{\frac{13.6}{16} }{\frac{13.6}{1} } =\frac{1}{16}=1:16$

Hence the ratio of their ionization energies is 1:16