Answer to Question #137977 in General Chemistry for Valeria Garcia

Question

if a firework gives off a bright orange color, what would the energy of a single photon be for this colored photon? assume that there we’re 3.50 moles of photon expelled by the explosion of the firework, what would the energy be in kj?

Answer 1

The orange colour of fireworks is due to the presence of calcium metal.

This orange colour has the wavelength, λ= 500 nm

= 500× 10^-9 m

We know that the energy of single photon , E =( hc/λ ) unit

h = plank's constant = 6.626×10^-34 J.s

c = velocity of light = 3×10^8 m/s

So, E =( hc/λ ) Joul

Or, E =[ ( 6.626×10^-34 J.s × 3×10^8 m.s-1) / 500× 10^-9 m ]

Or, E =[1.9878 ×10^-26/500× 10^-9] Joul

Or, E = 3.9756 × 10^-19 Joul

Hence,

the energy of a single photon be for this colored photon = 3.9756 × 10^-19 Joul

If there we’re, n= 3.50 moles of photon expelled by the explosion of the firework,

Then total energy = n×N_A×E Joul

Where,N_A = 6.023×10^23, E =(hc/λ) joul

= (3.50×6.023×10^23×3.9756 × 10^-19)/1000 kJ

= 838.076 kJ

Hence,

If there we’re, n= 3.50 moles of photon expelled by the explosion of the firework, then the total energy = 838.076 kJ