The number of photons required with a wavelength of 749 nm are needed to melt 445 g of ice is 5.12 × 10²³.
The energy of one photon is given as,
E = (h × C) / λ
E = (6.626 × 10⁻³⁴ × 3 × 10⁸ m/s) / (749 nm × 10⁻⁹ nm/m)
⇒ E = 0.02653 × 10⁻¹⁷ = 2.65 × 10⁻¹⁹ J
The enthalpy of fusion of water is 333.55 J/g.
To melt 445 g of ice, the energy needed = 445 g × 333.55 J/g = 135755 J
Hence, the number of photons required = (135755 J) / (2.65 × 10⁻¹⁹)
= 51228.301 × 10⁻¹⁹
= 5.12 × 10²³
Hence the number of photons required is 5.12 × 10²³.
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