How many photons at 553 nm must be absorbed to melt 380 102

How many photons at 553 nm must be absorbed to melt 3.80 × 102 g of ice? (Hint: It takes 334 J to melt 1 g of ice at 0°C.) Enter your answer in scientific notation. 3.54 × 10 23 photons On average, how many H2O molecules does one photon convert from ice to water? molecules

Solution

1)
1st calculate the heat required to melt all ice
Q = mass * Hfus
= 3.80*10^2 g * 334 J/g
= 1.27*10^5 J

Given:
lambda = 5.53*10^-7 m
1st calculate energy of 1 photon

use:
E = h*c/lambda
=(6.626*10^-34 J.s)*(3.0*10^8 m/s)/(5.53*10^-7 m)
= 3.595*10^-19 J

number of photon = total energy/energy of 1 photon
n = (1.27*10^5)/3.595*10^-19
= 3.53*10^23
Answer: 3.53*10^23 photons

2)

Molar mass of H2O,
MM = 2*MM(H) + 1*MM(O)
= 2*1.008 + 1*16.0
= 18.016 g/mol


mass(H2O)= 380 g

use:
number of mol of H2O,
n = mass of H2O/molar mass of H2O
=(380.0 g)/(18.016 g/mol)
= 21.09 mol
use:
number of molecules = number of mol * Avogadro’s number
number of molecules = 21.09 * 6.022*10^23 molecules
number of molecules = 1.27*10^25 molecules

number of molecules per photon = number of molecules/number of photon
= (1.27*10^25)/(3.53*10^23)
= 36.0
Answer: 36 molecules