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
![**Physics Problem: Photon Absorption by a Liquid**
A liquid is exposed to infrared radiation with a wavelength of \(9.51 \times 10^{-4}\) cm. Assume that all the radiation is absorbed and converted to heat. How many photons are required for the liquid to absorb 40.32 J of heat?
**Number of photons =** [Input box for calculation]
**Explanation:**
To solve this problem, we need to calculate the energy of a single photon and then determine how many photons are required to reach the total energy of 40.32 J.
1. **Energy of a Photon**:
The energy \(E\) of a single photon can be calculated using the formula:
\[
E = \frac{hc}{\lambda}
\]
where:
- \(h\) is Planck's constant \(6.63 \times 10^{-34} \text{ Js}\),
- \(c\) is the speed of light \(3.00 \times 10^{10} \text{ cm/s}\),
- \(\lambda\) is the wavelength \(9.51 \times 10^{-4} \text{ cm}\).
2. **Total Photons Required**:
Once the energy per photon is known, divide the total energy required by the energy of one photon:
\[
\text{Number of photons} = \frac{\text{Total energy required (J)}}{\text{Energy of one photon (J)}}
\]
This calculation will provide the number of photons needed for the liquid to absorb the given amount of heat.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1cab08ae-8e5c-4fa2-a89b-725536e38ab3%2F94e6bf81-b8a9-4830-b5c0-f7367ac1ddd2%2Fl3ttavh_processed.png&w=3840&q=75)
Transcribed Image Text:**Physics Problem: Photon Absorption by a Liquid**
A liquid is exposed to infrared radiation with a wavelength of \(9.51 \times 10^{-4}\) cm. Assume that all the radiation is absorbed and converted to heat. How many photons are required for the liquid to absorb 40.32 J of heat?
**Number of photons =** [Input box for calculation]
**Explanation:**
To solve this problem, we need to calculate the energy of a single photon and then determine how many photons are required to reach the total energy of 40.32 J.
1. **Energy of a Photon**:
The energy \(E\) of a single photon can be calculated using the formula:
\[
E = \frac{hc}{\lambda}
\]
where:
- \(h\) is Planck's constant \(6.63 \times 10^{-34} \text{ Js}\),
- \(c\) is the speed of light \(3.00 \times 10^{10} \text{ cm/s}\),
- \(\lambda\) is the wavelength \(9.51 \times 10^{-4} \text{ cm}\).
2. **Total Photons Required**:
Once the energy per photon is known, divide the total energy required by the energy of one photon:
\[
\text{Number of photons} = \frac{\text{Total energy required (J)}}{\text{Energy of one photon (J)}}
\]
This calculation will provide the number of photons needed for the liquid to absorb the given amount of heat.
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