According to the Bohr model for the hydrogen atom,the energy necessary to excite an electron from n = 7 to n = 8 is ____ the energy necessary to excite an electron from n = 5 to n = 6.
A) less than
B) greater than
C) equal to
D) either equal to or greater than
E) either less than or equal to

Question

Quizplus · Accepted Answer

According to the Bohr model, the energy of an electron in a hydrogen atom is given by E = -Rh/n^2, where Rh is the Rydberg constant and n is the principal quantum number. The energy difference between two levels is given by ΔE = E_final - E_initial = -Rh(1/n_final^2 - 1/n_initial^2), where n_final and n_initial are the principal quantum numbers of the final and initial states of the electron, respectively.

Using this formula, we can calculate the energy differences for the two transitions:

ΔE1 = -Rh(1/6^2 - 1/5^2) = -0.0875 Rh

ΔE2 = -Rh(1/8^2 - 1/7^2) = -0.051 Rh

We can see that ΔE2 is smaller than ΔE1, which means that less energy is required to excite an electron from n=7 to n=8 than from n=5 to n=6. Therefore, the answer is A) less than.

According to the Bohr Model for the Hydrogen Atom,the Energy