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Chapter 7: Problem 15

A photon has a wavelength of \(624 \mathrm{nm}\). Calculate the energy of the photon in joules.

Short Answer

Expert verified
The energy of the photon is \(3.18 \times 10^{-19} \, Joules\).

Step by step solution

01

Identification of Information

Identify what information is given. Here, the wavelength of the photon is given as \(624 \, nm\).
02

Convert Units

Convert the wavelength from nanometers to meters. It's important to use the correct units in the calculations. As 1 meter comprises 1 billion nanometers, we divide by 1 billion to do the conversion: \( \lambda = 624 \, nm = 624 \times 10^{-9} \, m\).
03

Apply Planck-Einstein Relation

Use the Planck-Einstein relation to calculate the energy of the photon. This equation is given by \(E = \frac{hc}{\lambda}\), where \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength. Planck's constant is \(6.626 \times 10^{-34} \, Js\) and the speed of light is \(2.998 \times 10^{8} \, m/s\). By substituting these values into the formula, we get \(E = \frac{(6.626 \times 10^{-34} \, Js)(2.998 \times 10^{8} \, m/s)}{624 \times 10^{-9} \, m}\).
04

Calculate Energy

Once the values are substituted into the formula, the next step is to calculate the energy. This gives \(E = 3.18 \times 10^{-19} \, Joules\).

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Most popular questions from this chapter

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