The most prominent line in the spectrum of aluminum is at 396.15 nm . What is the frequency of t

Name: Problem 7, Chapter 7: Chemistry and Chemical Reactivity
Uploaded: 2023-05-10T16:01:43-08:00
Channel: Ronald Prasad
Description: The most prominent line in the spectrum of aluminum is at 396.15 nm . What is the frequency of this line? What is the energy of one photon with this wavelength? Of 1.00 mol of these photons?

step 1 Starting with a given wavelength, 396 .15 nanometers, what is the frequency of this line? So the

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The most prominent line in the spectrum of aluminum is at $396.15 \mathrm{nm} .$ What is the frequency of this line? What is the energy of one photon with this wavelength? Of 1.00 mol of these photons?

   The most prominent line in the spectrum of aluminum is at $396.15 \mathrm{nm} .$ What is the frequency of this line? What is the energy of one photon with this wavelength? Of 1.00 mol of these photons?

Chemistry and Chemical Reactivity

John C. Kotz, Paul… 6th Edition

Chapter 7, Problem 7

Instant Answer

Solved by Expert Ronald Prasad

05/10/2023

Step 1

The frequency can be calculated using the formula: \[ \nu = \frac{c}{\lambda} \] where $ \nu $ is the frequency, $ c $ is the speed of light ($3.00 \times 10^8 \, m/s$), and $ \lambda $ is the wavelength (\(396.15 \, nm = 396.15 \times 10^{-9} \, Show more…

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The most prominent line in the spectrum of aluminum is at $396.15 \mathrm{nm} .$ What is the frequency of this line? What is the energy of one photon with this wavelength? Of 1.00 mol of these photons?

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Key Concepts

Wavelength-Frequency Relationship

This concept addresses the inherent link between a wave's wavelength and its frequency, encapsulated by the formula c = ?f, where c is the speed of light. It is fundamental for understanding how electromagnetic waves propagate and how one can be computed from the other.

Photon Energy Calculation

The energy of a photon is determined by Planck’s equation, E = hf, or equivalently E = hc/?. This relationship connects the energy carried by a photon directly to its frequency or inversely to its wavelength, illustrating the quantized nature of electromagnetic radiation.

Mole Concept and Avogadro’s Number

The mole is a unit that represents an amount of substance, and Avogadro’s number defines the number of entities (such as photons) in one mole. It is essential for scaling up calculations from a single particle to a macroscopic quantity, allowing one to compute the total energy in a given amount of moles.

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