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Chapter 7: Problem 17

A photon has a frequency of \(6.0 \times 10^{14} \mathrm{~Hz}\). (a) Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? (b) Calculate the energy (in joules) of this photon. (c) Calculate the energy (in joules) of 1 mole of photons all with this frequency.

Short Answer

Expert verified
The wavelength of the given frequency of a photon can be calculated using the formula for the speed of light. The energy of a single photon with this frequency and the energy of 1 mole of photons can be computed using Planck's formula and Avogadro's number, respectively.

Step by step solution

01

Conversion of Frequency into Wavelength

The wavelength (\(λ\)) in meters can be calculated using the following formula, where \(c\) is the speed of light and \(ν\) is the frequency: \( c = λν \). By rearranging this formula, we find: \( λ = c / ν \). Then, the obtained wavelength in meters should be converted into nanometers (1 meter = \(1 \times 10^9\) nm). Thus, \( λ(nm) = λ(m) \times 10^9 \). After this, it requires to check whether this wavelength falls into the visible region (approximately 400-700nm) or not.
02

Calculation of Photon Energy in Joules

The energy (E) of a photon in Joules can be calculated using Planck's formula, where \(h\) is Planck's constant and \(ν\) is the frequency: \( E = hν \).
03

Calculation of Energy in Joules for 1 Mole of Photons

The energy of 1 mole of photons can be calculated by multiplying the energy of one photon (obtained in Step 2) with Avogadro's number (approximately \(6.022 \times 10^{23}\) mol^-1), as each mole contains this amount of particles: \(E_{mole} = E_{photon} \times Avogadro's~number\).

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Most popular questions from this chapter

Use the Aufbau principle to obtain the ground-state electron configuration of technetium.

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