For the spectrum of the hydrogen atom, the Rydberg constant is given by . [where m = mass of electron, e = magnitude of fundamental charge, ε₀ = permittivity of vacuum, h = Planck's constant, c = velocity of light in vacuum]

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(4) R=(me⁴)/(8ε₀²h³c). Idea: in the Bohr model the energy of the nth level is Eₙ=-(me⁴)/(8ε₀²h²n²). A jump from n₂ down to n₁ emits a photon with (hc)/λ=E_n₂-E_n₁=(me⁴)/(8ε₀²h²)(1/(n₁²)-1/(n₂²)). Dividing by hc: 1/λ=(me⁴)/(8ε₀²h³c)(1/(n₁²)-1/(n₂²)). Comparing with 1/λ=R(1/(n₁²)-1/(n₂²)) gives R=(me⁴)/(8ε₀²h³c). Putting in the constants gives R≈1.097×10⁷ m⁻¹, the measured value.

For the spectrum of the hydrogen atom, the Rydberg constant is given by ______. [where m = mass of electron, e = magnitude of fundamental charge, ε₀ = permittivity of vacuum, h = Planck's constant, c = velocity of light in vacuum]

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Why the other options are wrong