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
