Question

Using the Bohr model, determine the energy in joules of the photon produced when an electron in a Li2+ ion moves from the orbit with n = 2 to the orbit with n = 1.

Answer 1

Answer:

1.64x10⁻¹⁸ J

Explanation:

By the Bohr model, the electrons surround the nucleus of the atom in shells or levels of energy. Each one has it's energy, and the electron doesn't fall to the nucleus because it can reach another level of energy, and then return to its level.

When the electrons go to another level, it absorbs energy, and then, when return, this energy is released, as a photon (generally as luminous energy). The value of the energy can be calculated by:

E = hc/λ

Where h is the Planck constant (6.626x10⁻³⁴ J.s), c is the light speed (3.00x10⁸ m/s), and λ is the wavelength of the photon.

The wavelength can be calculated by:

1/λ = R*(1/nf² - 1/ni²)

Where R is the Rydberg constant (1.097x10⁷ m⁻¹), nf is the final orbit, and ni the initial orbit. So:

1/λ = 1.097x10⁷ *(1/1² - 1/2²)

1/λ = 8.227x10⁶

λ = 1.215x10⁻⁷ m

So, the energy is:

E = (6.626x10⁻³⁴ * 3.00x10⁸)/(1.215x10⁻⁷)

E = 1.64x10⁻¹⁸ J