Question

A photon of 3000 A° is absorbed by a gas and then remitted as two photons one photon is red (λ=7600A°) what would be the wavelength of another photon?

Answer 1

Wavelength is 4972.5 Å

Step - by - step Explanation: Don't do mistake of directly subtracting both the wavelengths. Rather, find out the energy emitted because wavelength is neither emitted nor absorbed.

E = hc/λ

→ E = 6.63 × 10⁻ ³⁴ × 3 × 10⁸ × 1/7600 Å

→ E' = 6.63 × 10⁻ ³⁴ × 3 × 10⁸ × 1/3000 Å

→ E = 0.003 × 10⁻ ¹⁶ J

→ E' = 0.007 × 10⁻ ¹⁶ J

→ E' - E = 0.004 × 10⁻ ¹⁶ J = 4 × 10⁻ ¹⁹ J

→ 4 × 10⁻ ¹⁹ = 6.63 × 10⁻ ³⁴ × 3 × 10⁸/λ

→ λ = 4.9725 × 10⁻⁷

→ λ = 4972.5 Å