Chemistry 60 Help

Question

How many photons with a wavelength of 761 nm are needed to melt 405g of ice?

Number of photons?

Answer 1

To find heat energy needed to melt 405 g of ice, we use the formula q = m∆H_fusion

q = heat in joules

m = mass = 405 g

∆H_fusion = 334 J/g (look it up in a table)

q = (405 g)(334 J/g) = 135,270 J = 1.35x10⁵ J

The energy of 1 photon is given by E = hc/λ

We now know the energy needed is 1.35x10⁵ J. We can now determine how many photons with a wavelength of 761 nm it will take to deliver that energy.

E = hc/λ = (6.626x10^-34 Jsec)(3x10⁸ m/sec) / 761x10^-9 m

E = 2.61x10^-19 J / photon

1.35x10⁵ J x 1 photon / 2.61x10^-19 J = 5.17x10²³ photons needed