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Chapter 8: Problem 19

A certain radiation has a wavelength of \(574 \mathrm{nm}\). What is the energy, in joules, of (a) one photon; (b) a mole of photons of this radiation?

Short Answer

Expert verified
The energy of one photon and a mole of photons for the given radiation are roughly \(3.45 \times 10^{-19} \mathrm{J}\) and \(207.4 \mathrm{kJ/mol}\) respectively.

Step by step solution

01

Convert wavelength to meters

The wavelength is given in nanometres. Convert it to metres as energy calculations require the SI unit of length. There are \(1 \times 10^{-9}\) metres in one nanometre. So, \(574 \mathrm{nm} = 574 \times 10^{-9}\) metres.
02

Calculate the Energy of One Photon

Use the Planck-Einstein relation ((\(E = \frac{hc}{\lambda}\)) to calculate the energy of one photon. Here, \(h\) is the Planck's constant, \(6.63 \times 10^{-34} \mathrm{Js}\), \(c\) is the speed of light, \(3 \times 10^8 \mathrm{m/s}\), and \(\lambda\) is the wavelength. Plug in the values and solve for \(E\).
03

Calculate the Energy of a Mole of Photons

After energy of one photon is obtained, the energy of a mole of photons can be found by multiplying the energy of one photon with Avogadro's number (\(6.022 \times 10^{23} \mathrm{mole^{-1}}\)).

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Most popular questions from this chapter

Draw an energy-level diagram that represents all the possible lines in the emission spectrum of hydrogen atoms produced by electron transitions, in one or more steps, from \(n=5\) to \(n=1\).

Between which two orbits of the Bohr hydrogen atom must an electron fall to produce light of wavelength \(1876 \mathrm{nm} ?\)

In your own words, define the following terms or symbols: (a) \(\lambda ;\) (b) \(\nu ;\) (c) \(h ;\) (d) \(\psi ;\) (e) principal quantum number, \(n\).

Calculate the de Broglie wavelength, in nanometers, associated with a \(145 \mathrm{g}\) baseball traveling at a speed of \(168 \mathrm{km} / \mathrm{h} .\) How does this wavelength compare with typical nuclear or atomic dimensions?

Use appropriate relationships from the chapter to determine the wavelength of the line in the emission spectrum of \(\mathrm{He}^{+}\) produced by an electron transition from \(n=5\) to \(n=2\).
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