This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Another one hafsatjibril2006 — let's solve it. To find the wavelength of light in the Balmer series, we use the Rydberg formula: (1)/() = R ( (1)/(n_f^2) - (1)/(n_i^2) ) where: • is the wavelength • R is the Rydberg constant • n_f is the final principal quantum number • n_i is the initial principal quantum number Step 1: Identify the given values. For the Balmer series, the electron transitions to the n_f = 2 energy level. The given initial principal quantum number is n_i = 7. The Rydberg constant R = 1.097 × 10^-2 nm^-1. Step 2: Substitute the values into the Rydberg formula. (1)/() = (1.097 × 10^-2 nm^-1) ( (1)/(2^2) - (1)/(7^2) ) Step 3: Calculate the terms inside the parenthesis. (1)/() = (1.097 × 10^-2 nm^-1) ( (1)/(4) - (1)/(49) ) (1)/() = (1.097 × 10^-2 nm^-1) (0.25 - 0.02040816) (1)/() = (1.097 × 10^-2 nm^-1) (0.22959184) Step 4: Multiply by the Rydberg constant. (1)/() = 0.0025187 nm^-1 Step 5: Calculate the wavelength . = (1)/(0.0025187 nm)^-1 ≈ 397.02 nm Comparing this value with the given options, it matches option D. The final answer is D. 397.0 nm. What's next?