What is the wavelength of the K_α line for Mercury? A) 1.94 × 10^-11m B) 5.38 × 10^-12m C) 1.85 × 10^-11m D) 3.02 × 10^-12 m

Question

Quizplus · Accepted Answer

The K_α line for Mercury is emitted when an electron transitions from the L shell to the K shell. The wavelength of this line can be calculated using the Rydberg formula:$$\frac{1}{\lambda} = R_∞( \frac{1}{n_f^2} - \frac{1}{n_i^2})$$where R_∞ is the Rydberg constant, n_f is the final energy level (1 for the K shell), and n_i is the initial energy level (2 for the L shell). Plugging in these values, we get:$$\frac{1}{\lambda} = 1.097 × 10^7 m^{-1}( \frac{1}{1^2} - \frac{1}{2^2}) = 1.097 × 10^7 m^{-1}(1 - \frac{1}{4}) = 8.228 × 10^6 m^{-1}$$Taking the reciprocal of this value gives us the wavelength:$$\lambda = \frac{1}{8.228 × 10^6 m^{-1}} = 1.215 × 10^{-7} m$$This is the wavelength of the K_α line for Mercury.

What Is the Wavelength of the Kα Line for Mercury

What Is the Wavelength of the K_α Line for Mercury