Atomic emission, absorption of light and energy

Question

Consider the following energy levels of an atom:

E4 -1.0 x 10 E-19 J

E3 -5.0 x 10 E-19 J

E2 -10 x 10 E-19 J

E1 -15 x 10 E-19 J

What is the wavelength of the photon neede toecite an electron from E1 to E4?

What is the energy (J) a photon must have in order to excite an electron from E2 to E3?

When an electron drops from the E3 to the E1 level, the atom is said to undergo emission. Calculate the wavelength of the photon emitted in this process.

Answer 1

The wavelength of light is related to its energy via the equation...

E = hυ

Where υ is the frequency of light. Furthermore, the wavelength of light is inversely related to its frequency via...

υλ = c (speed of light)

Therefore the wavelength of a photon used to excite an electron from state E_n to E_m is based on the difference of energy needed.

To two decimal places...

E1 - E4 = 14 x10^-19 joules --> 6.626x10^-34 * 3x10⁸/ 14x10^-19 is the wavelength needed for this absorption process = 1.34x10^-7 meters= 134 nanometers

E3 - E2 = 5 x 10^-19 joules --> 6.626x10^-34 * 3x10⁸/ 5x10^-19 is the wavelength needed for this absorption process = 3.76x10^-7 meters = 376 nanometers

For the emission process of an ele tron falling from E3 to E1 yields...

E1 - E3 = 10x10^-19 joules --> 6.626x10^-34 * 3x10⁸ / 10x10^-19 is the wavelength from the emission = 1.88x10^-7 meters = 188 nanometers