Question

FIGURE Q38.12 shows the energy-level diagram of Element X.

a. What is the ionization energy of Element X?

b. An atom in the ground state absorbs a photon, then emits a photon with a wavelength of 1240 nm. What was the energy of the photon that was absorbed?

c. An atom in the ground state has a collision with an electron, then emits a photon with a wavelength of 1240 nm. What conclusion can you draw about the initial kinetic energy of the electron?

Short answer

$$\begin{gathered} a)\left|E_1\right|=4.0eV \\ b)E_{photon}=3.0eV \\ c)E_{elec}=3.0eV \end{gathered}$$

Step-by-step solution

Step 1. A figure showing energy-level diagram of Element X. 

We need to find out :

a) The ionization energy of Element X.

b) The energy of the photon that was absorbed when atom in the ground state absorbs a photon, then emits a photon with a wavelength of 1240 nm.

c) Conclusion about the initial kinetic energy of the electron when atom in the ground state has a collision with an electron, then emits a photon with a wavelength of 1240 nm.

Step 2. Solving on the basis of basic concepts of energy-level diagram.

a) The ionization energy of Element X is :

$\left|E_1\right|=-4-0=4.0eV$

b) $E_{photon}=3.0eV$because it has to go from n = 1 to n = 3 to emit 1240 nm photon.

c) $E_{elec}=3.0eV$because it also has to go from n = 1 to n = 3 to emit 1240 nm photon.