Answer
The total energy of photons detected in 1 hour is $6.448\times10^{-11}J$.
Work Step by Step
*Strategy:
1) Calculate the energy of a photon of this radiation.
2) Find the amount of energy of photons detected per second.
3) Figure out the total energy of photons detected in 1 hour.
1) Calculate the energy of a photon of this radiation.
- Wavelength of radiation: $\lambda=3.55\times10^{-3}m$
- Planck's constant: $h\approx6.626\times10^{-34}J.s$
- Speed of light in a vacuum: $c\approx2.998\times10^8m/s$
The energy of a photon of this radiation is:
$E_p=\frac{h\times c}{\lambda}=\frac{(6.626\times10^{-34})\times(2.998\times10^8)}{3.55\times10^{-3}}\approx5.596\times10^{-23}J$
2) Find the energy of photons detected per second.
- The number of photons detected per second: $N=3.2\times10^8photons/s$
The energy of photons detected per second is:
$E_s=E_p\times N= (5.596\times10^{-23})\times(3.2\times10^8)\approx1.791\times10^{-14}J/s$
3) Figure out the total energy of photons detected in 1 hour.
- Amount of time: $t=1h=3600s$
The total energy of photons detected in 1 hour is:
$E=E_s\times t=(1.791\times10^{-14})\times3600\approx6.448\times10^{-11}J$
