Consider the following portion of the energy-level diagram for hydrogen:
-The wavelength of light associated with the n = 2 to n = 1 electron transition in the hydrogen spectrum is 1.216 × 10^-7 m. By what coefficient should this wavelength be multiplied to obtain the wavelength associated with the same electron transition in the Li²⁺ ion?

Question

Consider the following portion of the energy-level diagram for hydrogen:

-The wavelength of light associated with the n = 2 to n = 1 electron transition in the hydrogen spectrum is 1.216 × 10^-7 m. By what coefficient should this wavelength be multiplied to obtain the wavelength associated with the same electron transition in the Li²⁺ ion?

Quizplus · Accepted Answer

The wavelength of light associated with electron transitions in hydrogen-like ions can be found using the Rydberg formula, which is inversely proportional to the square of the atomic number (Z) of the nucleus. For hydrogen (Z=1), the wavelength is given. For Li^2+ (lithium ion with a +2 charge), Z=3. Since the energy levels and thus the wavelengths depend on Z^2, moving from hydrogen (Z=1) to Li^2+ (Z=3) involves squaring 3, which gives 9. Therefore, the wavelength should be divided by 9 to account for the increased nuclear charge in Li^2+, making the correct answer 1/9.

Consider the Following Portion of the Energy-Level Diagram for Hydrogen