The ratio of wavelengths of H α H_{\alpha} H α and H β H_{\beta} H β lines in the Balmer series is x/20. Find x.

Question

The ratio of wavelengths of H α H_{\alpha} H α ​ and H β H_{\beta} H β ​ lines in the Balmer series is x/20. Find x.

G1 Physics · Accepted Answer

For Balmer-series lines: Hα corresponds to transition 3 → 2: 1/λ(α) = R[1/2² - 1/3²] = R(1/4 - 1/9) = 5R/36 So, λ(α) = 36/(5R) Hβ corresponds to transition 4 → 2: 1/λ(β) = R[1/4 - 1/16] = 3R/16 So, λ(β) = 16/(3R) Therefore, λ(α)/λ(β) = [36/(5R)]/[16/(3R)] = 108/80 = 27/20 Hence x = 27. Final value: 27

The ratio of wavelengths of H α H_{\alpha} H α ​ and H β H_{\beta} H β ​ lines in the Balmer series is x/20. Find x.

The ratio of wavelengths of H α H_{\alpha} H α and H β H_{\beta} H β lines in the Balmer series is x/20. Find x.