Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Calculate the number of quanta required to supply [tex]$7.06 \times 10^4 J[tex]$[/tex] of energy for heating [tex]$[/tex]235 \, g[tex]$[/tex] of water from [tex]$[/tex]22.6^{\circ} C[tex]$[/tex] to [tex]$[/tex]94.4^{\circ} C[tex]$[/tex] in a microwave oven with a frequency of [tex]$[/tex]2.88 \times 10^{10} \, s^{-1}$[/tex].

Sagot :

GinnyAnswer
To solve the problem, follow these steps:

1. Understand the Given Values:
- Energy required to heat the water (\(E_{\text{required}}\)): \(7.06 \times 10^4 \text{ J}\)
- Microwave frequency (\(\nu\)): \(2.88 \times 10^{10} \text{ Hz}\)

2. Use Planck’s Constant:
- Planck's constant (\(h\)): \(6.62607015 \times 10^{-34} \text{ J} \cdot \text{s}\)

3. Calculate the Energy of One Quantum (Photon):
- The energy (\(E_{\text{quantum}}\)) of one photon can be calculated using the formula:
[tex]\[ E_{\text{quantum}} = h \cdot \nu \][/tex]
- Plug in the values:
[tex]\[ E_{\text{quantum}} = (6.62607015 \times 10^{-34} \text{ J} \cdot \text{s}) \cdot (2.88 \times 10^{10} \text{ Hz}) \][/tex]
- Calculate:
[tex]\[ E_{\text{quantum}} = 1.9083082032 \times 10^{-23} \text{ J} \][/tex]

4. Calculate the Number of Quanta Required:
- The number of quanta (\(N\)) needed to supply the required energy is given by:
[tex]\[ N = \frac{E_{\text{required}}}{E_{\text{quantum}}} \][/tex]
- Plug in the values:
[tex]\[ N = \frac{7.06 \times 10^4 \text{ J}}{1.9083082032 \times 10^{-23} \text{ J}} \][/tex]
- Calculate:
[tex]\[ N = 3.6996120375949974 \times 10^{27} \][/tex]

Therefore, the number of quanta required to supply the [tex]\(7.06 \times 10^4 \text{ J}\)[/tex] of energy is approximately [tex]\(3.70 \times 10^{27}\)[/tex].
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.