A heat lamp produces 32.8 watts of power at a wavelength of 6.5 $\mu \mathrm{m}$. How many photons are emitted per second? (1 watt = 1 J/s)

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Quizlet Admin · Accepted Answer

So here, we are given the wavelength of a heat lamp which is 6.5 $\mu$m or $6.5	imes10^{-6}$ meters since micro($\mu$) is equal to $10^{-6}$. And the heat lamp produces 32.8 watts of power .

Wherein 1 watt is equal to 1 J/s.

We are required to find the number of photons in the heat lamp.

Using the formula:

$$
\begin{equation}E=\dfrac{hc}{\lambda} \end{equation}
$$

Where:

E= energy of a single photon

h= Planck's constant which is $6.626	imes10^{-34}$ J $\cdot$ s

c= speed of light which is 3.00$	imes10^{8}$ m/s

$\lambda$= wavelength

Therefore using equation (1) we can find the energy of a single photon.
$E=\dfrac{(6.626	imes10^{-34} 	ext{ J$\cdot$s})(3.00	imes10^{8} 	ext{m/s})}{6.5	imes10^{-6} 	ext{m}}$ 
$E=3.06	imes10^{-20}$ J 
Sincethe heat lamp produces 32.8 J/s of power we divide the energy of the laser pulse to the energy of a single photon. Thus,
$32.8 	ext{ J/s}	imes \dfrac{1 	ext{photon}}{3.06	imes10^{-20}	ext{J}}=\boxed{1.07	imes10^{21}	ext{ photons per seconds}}$

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Recommended textbook solutions

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