Answer
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Work Step by Step
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To determine if a photon of visible light (wavelength 400 to 700 nm) has enough energy to excite an electron in a hydrogen atom from the n = 1 to the n = 5 state, or from the n = 2 to the n = 6 state, we can use the Rydberg formula for the wavelengths of spectral lines:
1/λ = R (1/n1² - 1/n2²),
where R is the Rydberg constant (1.097 x 10⁷ m⁻¹), n1 and n2 are the lower and higher energy levels respectively.
1. For n = 1 to n = 5 transition: Substituting n1=1 and n2=5 in the Rydberg formula, we find the corresponding wavelength to be around 95 nm. This is outside the visible light spectrum (400-700 nm), so a visible light photon does not have sufficient energy for this transition.
2. For n = 2 to n = 6 transition: Substituting n1=2 and n2=6, we find the wavelength to be around 410 nm, which falls within the visible light range. Therefore, a visible light photon does have sufficient energy to excite an electron from n = 2 to n = 6 in a hydrogen atom.
