. Suppose an infrared photon with a wavelength of 853 nm were combined with another infrared photon with a wavelength of 865 nm, what would be the wavelength of the new 'combined' photon, in nm

Explanation:

Given the data in the question;

wavelength λ₁ = 853 nm = 853 × 10⁻⁹ m

wavelength λ₂ = 865 nm = 865 × 10⁻⁹ m

we determine the energy of each photons using the following expression;

= hc / λ

where h is Planck's constant ( 6.626 × 10⁻³⁴ J.s )

c is speed of light ( 3 × 10⁸ m/s )

For Photon with wavelength λ₁ = 853 × 10⁻⁹ m

= hc / λ

we substitute

= ( ( 6.626 × 10⁻³⁴ J.s )( 3 × 10⁸ m/s ) ) / (853 × 10⁻⁹ m)

= 1.9878 × 10⁻²⁵ / 853 × 10⁻⁹

= 2.33 × 10⁻¹⁹ J

For Photon with wavelength  λ₂ = 865 × 10⁻⁹ m

= ( ( 6.626 × 10⁻³⁴ J.s )( 3 × 10⁸ m/s ) ) / (865 × 10⁻⁹ m)

= 1.9878 × 10⁻²⁵ / 865 × 10⁻⁹

= 2.298 × 10⁻¹⁹ J

We know that; energy of the combined photon will be equal to the sum of energies of the two photons.

so

Energy of the combined photon = +

= 2.33 × 10⁻¹⁹ J + 2.298 × 10⁻¹⁹ J

 = 4.628 × 10⁻¹⁹ J

so wavelength of the new combined photon will be;

= hc / λ

λ = hc

λ = hc /

we substitute

λ = ( ( 6.626 × 10⁻³⁴ J.s )( 3 × 10⁸ m/s ) ) / 4.628 × 10⁻¹⁹ J

= 1.9878 × 10⁻²⁵ / 4.628 × 10⁻¹⁹

= 4.2952 × 10⁻⁷ m

= ( 4.2952 × 10⁻⁷ × 10⁹ )nm

= 429.5 nm

Therefore, Wavelength of the new 'combined' photon is 429.5 nm

definition

                    entropy is a measure of the randomness or the extent of disorder of a chemical process.

                      enthalpy is a measure of the heat change of a reaction occurring at a constant pressure.

measurement units:

                        entropy is measured in joule per kelvin (jk⁻¹)   whereas enthalpy is measured in joule per mole (jmol⁻¹)

requirements:

                            entropy has no requirements or limits, and its change is measured by the division between the heat change of the chemical process and the temperature.

                              in contrast, enthalpy can only be related to the heat change of the reaction under standard conditions.