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  • A 100 W light bulb emits photons per second. Determine emitted photons waveleng

A 100 W light bulb emits 5.0 \times 10^{18} photons per second. Determine emitted photons wavelength? \left(\right.$ Take $h=6.6 \times 10^{-34} \mathrm{Js} and \left.c=3.0 \times 10^8 \mathrm{~m} / \mathrm{s}\right)

Option: 1

400 nm

 


Option: 2

990 nm


Option: 3

600 nm

 


Option: 4

700 nm


Answers (1)

best_answer

The number of photons emitted per second can be calculated using the formula n=P /E, where P is the power of the source and E is the energy of each photon. Rearranging this equation gives E=P / n.
Therefore, the energy of each photon can be calculated as:
\begin{aligned} & E=\frac{P}{n}=\frac{100 \mathrm{~W}}{5.0 \times 10^{18} \text { photons } / \mathrm{s}}=2 \times 10^{-20} \mathrm{~J} \end{aligned}
The energy of a photon can also be calculated using the equation E=\frac{h c}{\lambda}, where \mathrm{h} is Planck's constant, \mathrm{c} is the speed of light, and \lambda is the wavelength of light. Rearranging this equation gives \lambda=h c / E.
Therefore, the wavelength of the emitted photons can be calculated as:
$$ \begin{aligned} & \lambda=\frac{h c}{E}=\frac{\left(6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}\right)\left(3.0 \times 10^8 \mathrm{~m} / \mathrm{s}\right)}{2 \times 10^{-20} \mathrm{~J}}= 9.9 \times 10^{-8} \mathrm{~m} \end{aligned}
Converting to nanometers gives:
$$ \lambda=9.9 \times 10^{-8} \mathrm{~m} \times \frac{1 \mathrm{~nm}}{10^{-9} \mathrm{~m}}=990 \mathrm{~nm}
 

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