Question

# A sodium incandescent bulb emits $589nm$ wavelength light at $60watts$. calculate the number of photons emitted by the bulb.

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Solution

## Step1: Given dataThe wavelength of the sodium incandescent bulb light is $\lambda =589×{10}^{-9}m.$The total energy of the light is $E=60watt.$The energy of each photon of wavelength $\lambda$ is defined by the form $E=\frac{hc}{\lambda }$, where, h is the Plank constant and c is the velocity of light in free space.Step 2: Finding the number of photonsLet there be n number of photons exist in the $60watt$ light.The energy of one photon is $E=\frac{hc}{\lambda }$.So, $E=\frac{hc}{\lambda }=\frac{\left(6.626×{10}^{-34}\right)×\left(3×{10}^{8}\right)m/{s}^{-1}}{589×{10}^{-8}m}=3.37×{10}^{-20}\because \left(c=speedoflight=3×{10}^{8}m/{s}^{-1}\right)\phantom{\rule{0ex}{0ex}}orE=3.37×{10}^{-20}watt.$So, the number of photons is $n=\frac{Totalenergyoflightsource}{Energyofeachphoton}=\frac{60}{3.37×{10}^{-20}}=1.7×{10}^{21}\phantom{\rule{0ex}{0ex}}orn=1.7×{10}^{21}$Therefore, the number of photons emitted by the bulb is $1.7×{10}^{21}$.

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