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Construct an energy level diagram for a doubly-ionized Lithium atom (z=3, 1 electron). What are the...

Construct an energy level diagram for a doubly-ionized Lithium atom (z=3, 1 electron). What are the possible frequencies of light emitted for the electron moving around between the first three energy levels? (there are three answers)

Expert Solution

Below is the Energy Level diagram of doubly ionized Li.

In the above diagram, n represents the energy level, vertical axis - energies and vertical lines with the arrows represent possible transitions. Energy levels are calculated using Bohr's formula,

E_n = -13.6 (Z²/ n²) eV

Now, frequency of light emitted due to electron transition between first 3 energy levels can be calculated using the formula,

E = hf

Thus, f= E/h

In the above formula, we replace E by E, the difference between two energy states.

1. Electron transition from n=3 to n=2

f = (-13.6 + 30.6) * 1.6 *10^-19/ (6.626 * 10^-34) Hz (We have used the value 1eV = 1.6 *10^-19 J )

f = 4.105 * 10¹⁵ Hz

2. Electron transition from n=2 to n=1

f = (-30.6 + 122.4) * 1.6 *10^-19/ (6.626 * 10^-34) Hz

f = 22.167 * 10¹⁵ Hz

3. Electron transition from n=3 to n=1

f = (-13.6 + 122.4) * 1.6 *10^-19/ (6.626 * 10^-34) Hz

f = 26.272 * 10¹⁵ Hz

genius_generous answered 2 hours ago

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