About #3.94*10^(20)# photons

First find the energy of the photon

#E=hf#

where #h=6.63*10^(-34)# Planck's constant and #f# is the frequency of the radiation. You are given wavelength so that needs to be converted.

#E=h*c/lambda#

#=6.63*10^(-34)*(3.00*10^8)/(3.0*10^-6)#

note #c# is the speed of light and the wavelength #lambda# given is converted to meters

#E=6.363*10^(-20)# Joules

This is the energy per photon. The energy required to raise the temperature of the water can be determined by

#Q=mcDeltaT#

where #m# is the mass of water 2.5 g; #c# is the specific heat capacity value #4.18 Jg^(-1)K^(-1)#; and #DeltaT# is the temperature change 2.4 K

#Q=(2.5)(4.18)(2.4) = 25.08# Joules

Now divide the required energy by the energy per photon to get the number of photons (it will be a large number)

#(25.08)/(6.363*10^(-20))=3.94*10^(20)# photons