- A photon has an energy of 5.00×10-19 Joules. What is its wavelength in nm ? B) The frequer ansition is 5.4×10¹5 Hz. What is the corresponding energy? Which region corresponds to this' h= 6.62X10-34 J/s)
- A photon has an energy of 5.00×10-19 Joules. What is its wavelength in nm ? B) The frequer ansition is 5.4×10¹5 Hz. What is the corresponding energy? Which region corresponds to this' h= 6.62X10-34 J/s)
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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![### Photon Energy and Wavelength Calculation
#### Problem Statement
1. A photon has an energy of \( 5.00 \times 10^{-19} \) Joules. What is its wavelength in nm?
2. The frequency of a transition is \( 5.4 \times 10^{15} \) Hz.
- What is the corresponding energy?
- Which region of the electromagnetic spectrum corresponds to this transition?
Given the constant \( h = 6.62 \times 10^{-34} \) J·s.
---
#### Solution Overview
1. **Determine the Wavelength in nm for the Photon Energy:**
The energy \( E \) of a photon is related to its wavelength \( \lambda \) by the equation:
\[
E = \frac{hc}{\lambda}
\]
where \( h \) is Planck's constant and \( c \) is the speed of light (approximately \( 3.00 \times 10^8 \) m/s).
2. **Calculate the Energy Corresponding to the Given Frequency:**
The relationship between the energy \( E \) and the frequency \( f \) is given by:
\[
E = hf
\]
3. **Identify the Electromagnetic Spectrum Region:**
By determining the wavelength of the photon, or by analyzing the frequency, it is possible to classify it within a region of the electromagnetic spectrum, such as ultraviolet, visible light, infrared, etc.
##### Steps to Solve:
- **Step 1: Calculate Wavelength (in nm) from Energy**
\[
E = \frac{hc}{\lambda} \implies \lambda = \frac{hc}{E}
\]
Substituting the given values:
\[
\lambda = \frac{(6.62 \times 10^{-34} \, \text{J·s})(3.00 \times 10^8 \, \text{m/s})}{5.00 \times 10^{-19} \, \text{J}}
\]
Solving the expression will provide the wavelength in meters, which can then be converted to nanometers (1 nm = \( 10^{-9} \) meters).
- **Step 2: Calculate Energy from Frequency**
\[
E = hf
\]
Substituting the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93201fca-5730-4e6e-9e15-3568f7e0d408%2Fae4daee0-054d-46a2-b11b-96b71e47b886%2Fdprfscl_processed.png&w=3840&q=75)
Transcribed Image Text:### Photon Energy and Wavelength Calculation
#### Problem Statement
1. A photon has an energy of \( 5.00 \times 10^{-19} \) Joules. What is its wavelength in nm?
2. The frequency of a transition is \( 5.4 \times 10^{15} \) Hz.
- What is the corresponding energy?
- Which region of the electromagnetic spectrum corresponds to this transition?
Given the constant \( h = 6.62 \times 10^{-34} \) J·s.
---
#### Solution Overview
1. **Determine the Wavelength in nm for the Photon Energy:**
The energy \( E \) of a photon is related to its wavelength \( \lambda \) by the equation:
\[
E = \frac{hc}{\lambda}
\]
where \( h \) is Planck's constant and \( c \) is the speed of light (approximately \( 3.00 \times 10^8 \) m/s).
2. **Calculate the Energy Corresponding to the Given Frequency:**
The relationship between the energy \( E \) and the frequency \( f \) is given by:
\[
E = hf
\]
3. **Identify the Electromagnetic Spectrum Region:**
By determining the wavelength of the photon, or by analyzing the frequency, it is possible to classify it within a region of the electromagnetic spectrum, such as ultraviolet, visible light, infrared, etc.
##### Steps to Solve:
- **Step 1: Calculate Wavelength (in nm) from Energy**
\[
E = \frac{hc}{\lambda} \implies \lambda = \frac{hc}{E}
\]
Substituting the given values:
\[
\lambda = \frac{(6.62 \times 10^{-34} \, \text{J·s})(3.00 \times 10^8 \, \text{m/s})}{5.00 \times 10^{-19} \, \text{J}}
\]
Solving the expression will provide the wavelength in meters, which can then be converted to nanometers (1 nm = \( 10^{-9} \) meters).
- **Step 2: Calculate Energy from Frequency**
\[
E = hf
\]
Substituting the
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