The Photon, the Quantum of Light — Question 10

Question 10

Calorimetry and photon counting jointly infer wavelength and absorption

A monochromatic pulse deposits $Q=3.20\,\mathrm{nJ}$ in a calorimeter. An independent measurement gives $N_{\mathrm{abs}}=10^{10}$ absorbed photons and $N_{\mathrm{in}}=2.00\times10^{10}$ incident photons. Assume all absorbed optical energy becomes measured heat. Use $hc=1240\,\mathrm{eV\,nm}$ and $1\,\mathrm{eV}=1.60\times10^{-19}\,\mathrm J$.

1. Infer photon energy and wavelength.

2. Find the absorption fraction and total incident pulse energy.

Question 10 - Solution

Calorimetry and photon counting jointly infer wavelength and absorption

(a) Method and calculation

$$E_\gamma=Q/N_{\mathrm{abs}}=3.20\times10^{-19}\,\mathrm J=\boxed{2.00\,\mathrm{eV}}.$$$$\boxed{\lambda=hc/E_\gamma=620\,\mathrm{nm}}.$$

(b) Interpretation and further calculation

$$\boxed{a=N_{\mathrm{abs}}/N_{\mathrm{in}}=.500}.$$$$\boxed{U_{\mathrm{in}}=N_{\mathrm{in}}E_\gamma=6.40\,\mathrm{nJ}},\quad Q=aU_{\mathrm{in}}.$$

Physical check

The wavelength inference uses absorbed photons, while the absorption fraction compares absorbed and incident counts.