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...
Related questions
Question
![**Question:**
Calculate the frequency in hertz of electromagnetic radiation that has a wavelength of 534.0 nm. (c = 3.00 x 10^8 m/s)
**Explanation:**
To find the frequency (f) of electromagnetic radiation, use the formula:
\[ f = \frac{c}{\lambda} \]
where:
- \( c \) is the speed of light (3.00 x 10^8 m/s)
- \( \lambda \) is the wavelength in meters.
First, convert the wavelength from nanometers to meters:
\[ 534.0 \text{ nm} = 534.0 \times 10^{-9} \text{ m} \]
Now, substitute the values into the formula:
\[ f = \frac{3.00 \times 10^8 \text{ m/s}}{534.0 \times 10^{-9} \text{ m}} \]
Use a calculator to solve for \( f \), which will give you the frequency in hertz.
**Interactive Calculator:**
On the right side of the image, there is a basic calculator interface visible on a laptop screen. This calculator can be used to input the equation and perform the calculation to determine the frequency. The calculator includes the following features:
- Number buttons (0-9)
- Basic arithmetic operations (multiplication, clear, positive/negative toggle)
- A button for scientific notation (x 10)
- An indicator for the unit of frequency (\( s^{-1} \), hertz).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81a44892-e725-436e-9c8e-21f599a0ba84%2Fa5c32155-80cd-42c0-a097-187a35c2a088%2Fjihcm8u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Calculate the frequency in hertz of electromagnetic radiation that has a wavelength of 534.0 nm. (c = 3.00 x 10^8 m/s)
**Explanation:**
To find the frequency (f) of electromagnetic radiation, use the formula:
\[ f = \frac{c}{\lambda} \]
where:
- \( c \) is the speed of light (3.00 x 10^8 m/s)
- \( \lambda \) is the wavelength in meters.
First, convert the wavelength from nanometers to meters:
\[ 534.0 \text{ nm} = 534.0 \times 10^{-9} \text{ m} \]
Now, substitute the values into the formula:
\[ f = \frac{3.00 \times 10^8 \text{ m/s}}{534.0 \times 10^{-9} \text{ m}} \]
Use a calculator to solve for \( f \), which will give you the frequency in hertz.
**Interactive Calculator:**
On the right side of the image, there is a basic calculator interface visible on a laptop screen. This calculator can be used to input the equation and perform the calculation to determine the frequency. The calculator includes the following features:
- Number buttons (0-9)
- Basic arithmetic operations (multiplication, clear, positive/negative toggle)
- A button for scientific notation (x 10)
- An indicator for the unit of frequency (\( s^{-1} \), hertz).
![**Question:**
What is the energy of a mole of photons that have a wavelength of 473 nm?
Given:
- Planck's constant \( h = 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \)
- Speed of light \( c = 3.00 \times 10^8 \, \text{m/s} \)
**Explanation:**
To calculate the energy of a mole of photons, use the formula for energy of a photon:
\[ E = \frac{h \cdot c}{\lambda} \]
Where:
- \( E \) is the energy of one photon
- \( h \) is Planck's constant
- \( c \) is the speed of light
- \( \lambda \) is the wavelength in meters
To find the energy per mole, use Avogadro's number (\(6.022 \times 10^{23} \, \text{mol}^{-1}\)) and multiply the energy of one photon by this number.
**Diagram:**
The image also contains a numeric keypad on the right side, which would typically allow the user to input numerical answers or calculations directly on a screen-based calculator tool. There are numbered buttons (1-9), along with operational keys for basic functions, a decimal point, and a backspace key. However, these elements do not affect the calculation process described above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81a44892-e725-436e-9c8e-21f599a0ba84%2Fa5c32155-80cd-42c0-a097-187a35c2a088%2Fkckcwc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
What is the energy of a mole of photons that have a wavelength of 473 nm?
Given:
- Planck's constant \( h = 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \)
- Speed of light \( c = 3.00 \times 10^8 \, \text{m/s} \)
**Explanation:**
To calculate the energy of a mole of photons, use the formula for energy of a photon:
\[ E = \frac{h \cdot c}{\lambda} \]
Where:
- \( E \) is the energy of one photon
- \( h \) is Planck's constant
- \( c \) is the speed of light
- \( \lambda \) is the wavelength in meters
To find the energy per mole, use Avogadro's number (\(6.022 \times 10^{23} \, \text{mol}^{-1}\)) and multiply the energy of one photon by this number.
**Diagram:**
The image also contains a numeric keypad on the right side, which would typically allow the user to input numerical answers or calculations directly on a screen-based calculator tool. There are numbered buttons (1-9), along with operational keys for basic functions, a decimal point, and a backspace key. However, these elements do not affect the calculation process described above.
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