# Question #ca3af

Apr 10, 2015

About $3.94 \cdot {10}^{20}$ photons

First find the energy of the photon

$E = h f$

where $h = 6.63 \cdot {10}^{- 34}$ Planck's constant and $f$ is the frequency of the radiation. You are given wavelength so that needs to be converted.

$E = h \cdot \frac{c}{\lambda}$
$= 6.63 \cdot {10}^{- 34} \cdot \frac{3.00 \cdot {10}^{8}}{3.0 \cdot {10}^{-} 6}$

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

$E = 6.363 \cdot {10}^{- 20}$ Joules

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

$Q = m c \Delta T$

where $m$ is the mass of water 2.5 g; $c$ is the specific heat capacity value $4.18 J {g}^{- 1} {K}^{- 1}$; and $\Delta T$ is the temperature change 2.4 K

$Q = \left(2.5\right) \left(4.18\right) \left(2.4\right) = 25.08$ Joules

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

$\frac{25.08}{6.363 \cdot {10}^{- 20}} = 3.94 \cdot {10}^{20}$ photons