The wavelength of light associated with the n = 2 to n = 1 electron transition in the hydrogen spectrum is 1.216 $\times$ 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? A)1/9 B)1/7 C)1/4 D)1/3 E)1

Question

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 for the n=2 to n=1 transition is given. For Li²⁺ (Z=3), the effective nuclear charge is three times that of hydrogen, so the wavelength should be divided by 3² (since the energy levels scale as Z² for hydrogen-like ions), which is 9. Therefore, the correct coefficient is 1/9.

The Wavelength of Light Associated with the N = 2 ×\times×

The Wavelength of Light Associated with the N = 2 $\times$