In a certain electronic transition from the quantum level, 'n' to the ground state in atomic hydrogen in one or more steps, no linebelonging to the Brackett series is observed. What wave numbers may be observed in the
Balmer series? (R=Rydberg Constant)

Since no Brackett series lines are observed, the initial quantum level must be n ≤ 4 (otherwise Brackett series would appear).

All possible transitions when n = 4:

• 4 → 3
• 4 → 2
• 4 → 1
• 3 → 2
• 3 → 1
• 2 → 1

Balmer Series Transitions

Balmer series lines are produced when electrons fall to the second shell (n_f = 2):

• 4 → 2
• 3 → 2

Wave Number Calculations

(i) For transition 4 → 2:

ν̃₁ = R_H [¹⁄_2² - ¹⁄_4²] = R_H [¹⁄₄ - ¹⁄₁₆] = ³⁄₁₆ R_H

(ii) For transition 3 → 2:

ν̃₂ = R_H [¹⁄_2² - ¹⁄_3²] = R_H [¹⁄₄ - ¹⁄₉] = ⁵⁄₃₆ R_H

Final Answer

The possible observed Balmer series wave numbers are: ³⁄₁₆ R_H and ⁵⁄₃₆ R_H

Where R_H is the Rydberg constant for hydrogen.