An atom absorbs a photon of wavelength 500 nm and emits another photon of wavelength 600 nm. The net energy absorbed is n × 10⁻⁴ eV. Find n. Take h = 6.6 × 10⁻³⁴ J s and c = 3 × 10⁸ m s⁻¹.
Physics · Atomic Structure and X-rays · atomic structre and bohr atomic model
13 April 2023 Evening Shift

Question

An atom absorbs a photon of wavelength 500 nm and emits another photon of wavelength 600 nm. The net energy absorbed is n × 10⁻⁴ eV. Find n. Take h = 6.6 × 10⁻³⁴ J s and c = 3 × 10⁸ m s⁻¹.

Physics · Atomic Structure and X-rays · atomic structre and bohr atomic model

13 April 2023 Evening Shift

G1 Physics · Accepted Answer

Net energy absorbed: ΔE = hc(1/λ₁ - 1/λ₂) where λ₁ = 500 nm λ₂ = 600 nm Thus, ΔE = (6.6 × 10⁻³⁴)(3 × 10⁸) [1/(500 × 10⁻⁹) - 1/(600 × 10⁻⁹)] = 6.6 × 10⁻²⁰ J Convert to electron-volt using 1 eV = 1.6 × 10⁻¹⁹ J ΔE = (6.6 × 10⁻²⁰)/(1.6 × 10⁻¹⁹) = 0.4125 eV = 4125 × 10⁻⁴ eV Therefore n = 4125. Final answer: 4125.