Final answer:
To melt 3.40 g of ice, you would need approximately 3.80 x 10^4 photons of wavelength 5.98 x 10^(-6)m.
Step-by-step explanation:
The amount of heat required to melt the ice is given by the equation Q = mL
The molar mass of ice (H2O) is 18.015 g/mol. So, the number of moles in 3.40 g of ice is 3.40 g / 18.015 g/mol = 0.189 mol.
Next, we will use Avogadro's number (6.022 x 1023 mol-1) to convert moles to particles. The number of particles in 0.189 mol of ice is 0.189 mol x 6.022 x 1023 particles/mol = 1.136 x 1023 particles.
Finally, we can use the energy equation E = hc/λ, where E is the energy of one photon, h is Planck's constant (6.626 x 10-34 J s), c is the speed of light (3.00 x 108 m/s), and λ is the wavelength of the photons (5.98 x 10-6 m). Plugging in the values, we get E = (6.626 x 10-34 J s x 3.00 x 108 m/s) / (5.98 x 10-6 m) = 3.35 x 10-19 J.
Therefore, the number of photons required to melt 3.40 g of ice is 1.136 x 1023 particles x (3.35 x 10-19 J / 1 particle) = 3.80 x 104 photons.