Answer:
ni = approx 1
Step-by-step explanation:
speed of light c = fλ where is the the corresponding frequency and λ is the wavelength.
λ = 434 nm, 1 nm = 1/ 10⁹ m
3.00 × 10⁸ m/s = (434 / 10 ⁹) m × f
f = 3.00 × 10⁸ × 10⁹) / 434 = 6.9124 × 10 ¹⁴ Hz
Energy = hf where h is planck constant = 6.62 × 10⁻³⁴ J.s
E = 6.62 × 10⁻³⁴ J.s × 6.9124 × 10 ¹⁴ Hz = 4.76 × 10⁻¹⁹J
In a hydrogen atom, the energy of the photon emitted can be calculated using the formula below:
ΔE = RH ( 1/ ni² - 1/nf²)
4.76 × 10⁻¹⁹J = 2.18 × 10⁻¹⁸ J ( 1/ ni² - 1/nf²)
(4.76 × 10⁻¹⁹J) / (2.18 × 10⁻¹⁸ J) = ( 1/ ni² - 1/nf²)
0.21835 = 1/ni² - 1/ 2²
0.21835 + 0.25 = 1/ni²
0.46835 = 1/ni²
ni² = 1 / 0.46835 = 2.135155
ni = √2.135155 = 1.46 approx 1