Question

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

a) 2.04 × 10^–18 J
b) 4.08 × 10^–18 J
c) 8.16 × 10^–18 J
d) 1.63 × 10^–17 J

Answer 1

The energy of the photon produced when an electron transitions from n=2 to n=1 in a Li2+ ion is 2.04 × 10–18 J, as calculated using the Bohr model. The correct answer is a) 2.04 × 10^–18 J.

Step-by-step explanation:

To 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 using the Bohr model, we use the formula for the energy change associated with an electron transition:

E = -R(H) * Z2 * (1/nf2 - 1/ni2)

Where:

• R(H) is the Rydberg constant for hydrogen (2.18 × 10-18 J)
• Z is the atomic number of lithium (3 for Li2+)
• nf is the final quantum number (1 for the n=1 orbit)
• ni is the initial quantum number (2 for the n=2 orbit)

Substituting the values we have:

E = -2.18 × 10-18 J * 32 * (1/12 - 1/22)

After the calculations, we find that the energy of the photon is 2.04 × 10–18 J, which corresponds to option (a).