Question

Calculate the energy, in joules, required to excite a hydrogen atom by causing an electronic

transition from the n = 1 to the n = 4 principal energy level. Recall that the energy levels of the H

atom are given by En = -2.18 × 10-18 J(1/n2).

O 2.07 x 10^-29 J

O 2.25 x 10^-18 J

O 2.19 x 10^5 J

O 3.27 x 10^-17 J

O 2.04 x 10^-18 J

Answer 1

The energy required to excite a hydrogen atom from the n = 1 to the n = 4 level is calculated as 2.04 x 10^-18 J.

Step-by-step explanation:

The task involves calculating the energy required to transition an electron from the n = 1 energy level to the n = 4 energy level in a hydrogen atom. Using the provided formula En = -2.18 × 10-18 J(1/n2), we can find the energy of the electron at both levels and then determine the energy difference to find the transition energy.

First, we calculate the energies for n=1 and n=4:

• For n=1: E1 = -2.18 × 10-18 J × (1/12) = -2.18 × 10-18 J
• For n=4: E4 = -2.18 × 10-18 J × (1/42) = -2.18 × 10-18 J × (1/16) = -0.13625 × 10-18 J

Then, the energy required for the transition is the difference E4 - E1:

Energy required = E1 - E4 = (-2.18 × 10-18 J) - (-0.13625 × 10-18 J) = -2.04375 × 10-18 J

The negative sign indicates the energy gained by the atom, but since the question is asking for energy required, we consider the positive value:

Energy required = 2.04375 × 10-18 J

The correct answer from the options provided is therefore 2.04 x 10-18 J.