Respuesta :
Answer:
As we look at higher and higher electron shells, they get farther and farther apart, but the difference in energy between them gets smaller and smaller.
Explanation:
The final option is the only correct option. We can get to the answer directly by looking at equations for Bohr's model. Let us look at the radius and energy equations separately.
- Radius in the Bohr model: According to Bohr's model, the radius of an electron shell is directly proportional to the square of the index (n) of the shell and inversely proportional to the the atomic number (Z) of the element. The exact equation is: [tex]r_{n} = 0.0529\frac{n^{2}}{Z}[/tex] nm. Let us take the atom of hydrogen so that Z=1. Therefore, [tex]r_{n} = 0.0529n^{2}[/tex] nm. Thus, the first shell (n=1) has a radius of 0.0529nm, the second shell(n=2) has a radius of 4×0.0529 nm and the thirds has a radius of 9×0.0529 nm. So, we can see that the difference between the radius keeps on increasing as we keep increasing n (or moving to higher shells).
- Energy in the Bohr model: According to Bohr's model, energy of a shell is directly proportional to square of the atomic number of the element and inversely proportional to the square of the index of the shell. The exact equation is: [tex]E_{n} = -13.6\frac{Z^{2}}{n^{2}}[/tex] eV. Now, taking Z = 1 (hydrogen atom) for simplicity, as we keep on increasing the value of n, the denominator in the above equation keeps on increasing and hence, the energy decreases. As 'n' increases according to the square function, the value of E decreases more as n increases. Hence, the difference between energy of the shells decreases as n increases (or moving to higher shells)
