Vitamin D is produced in the skin when 7-dehydrocholesterol reacts with UVB rays (ultraviolet B) having wavelengths between 270 nm and 300 nm. What is the energy range Emin
Vitamin D is produced in the skin when 7-dehydrocholesterol reacts with UVB rays (ultraviolet B) having wavelengths between 270 nm and 300 nm. What is the energy range Emin
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Question
![### Vitamin D Production and UVB Photons
Vitamin D is produced in the skin when 7-dehydrocholesterol reacts with UVB rays (ultraviolet B) having wavelengths between 270 nm and 300 nm. What is the energy range \( E_{\text{min}} \leq E \leq E_{\text{max}} \) of the UVB photons?
#### Energy Calculation
To find the energy range of the UVB photons, we use the formula relating energy \( E \), wavelength \( \lambda \), and the Planck constant \( h \):
\[ E = \frac{hc}{\lambda} \]
Where:
- \( h \approx 6.626 \times 10^{-34} \, \text{Js} \) (Planck's constant)
- \( c \approx 3 \times 10^8 \, \text{m/s} \) (speed of light)
#### Determine \( E_{\text{min}} \) and \( E_{\text{max}} \)
1. **Calculate \( E_{\text{min}} \) for \( \lambda = 300 \, \text{nm} \):**
\[
E_{\text{min}} = \frac{hc}{300 \times 10^{-9} \, \text{m}}
\]
2. **Calculate \( E_{\text{max}} \) for \( \lambda = 270 \, \text{nm} \):**
\[
E_{\text{max}} = \frac{hc}{270 \times 10^{-9} \, \text{m}}
\]
#### Input Fields
- \( E_{\text{min}} \) = [________] J
- \( E_{\text{max}} \) = [________] J
This exercise allows students to calculate the energy of photons based on their wavelength and understand the relationship between energy, wavelength, and the physical constants involved.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F245e0eb4-5097-4578-8f56-633b47cf5980%2Fda92e598-8cc3-4c0f-b8b6-809025fb5999%2Fzx4b4kl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Vitamin D Production and UVB Photons
Vitamin D is produced in the skin when 7-dehydrocholesterol reacts with UVB rays (ultraviolet B) having wavelengths between 270 nm and 300 nm. What is the energy range \( E_{\text{min}} \leq E \leq E_{\text{max}} \) of the UVB photons?
#### Energy Calculation
To find the energy range of the UVB photons, we use the formula relating energy \( E \), wavelength \( \lambda \), and the Planck constant \( h \):
\[ E = \frac{hc}{\lambda} \]
Where:
- \( h \approx 6.626 \times 10^{-34} \, \text{Js} \) (Planck's constant)
- \( c \approx 3 \times 10^8 \, \text{m/s} \) (speed of light)
#### Determine \( E_{\text{min}} \) and \( E_{\text{max}} \)
1. **Calculate \( E_{\text{min}} \) for \( \lambda = 300 \, \text{nm} \):**
\[
E_{\text{min}} = \frac{hc}{300 \times 10^{-9} \, \text{m}}
\]
2. **Calculate \( E_{\text{max}} \) for \( \lambda = 270 \, \text{nm} \):**
\[
E_{\text{max}} = \frac{hc}{270 \times 10^{-9} \, \text{m}}
\]
#### Input Fields
- \( E_{\text{min}} \) = [________] J
- \( E_{\text{max}} \) = [________] J
This exercise allows students to calculate the energy of photons based on their wavelength and understand the relationship between energy, wavelength, and the physical constants involved.
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