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Ch.8 - The Quantum-Mechanical Model of the Atom
Tro - Chemistry: A Molecular Approach 5th Edition
Tro5th EditionChemistry: A Molecular ApproachISBN: 9780134874371당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Tro 5th EditionCh.8 - The Quantum-Mechanical Model of the Atom문제 91
8장, 문제 91

A laser produces 20.0 mW of red light. In 1.00 hr, the laser emits 2.29×1020 photons. What is the wavelength of the laser?

검증된 단계별 안내
1
Identify the given values: Power (P) = 20.0 mW, Time (t) = 1.00 hr, Number of photons (N) = 2.29 \(\times\) 10^{20}.
Convert the power from milliwatts to watts: 1 mW = 0.001 W, so 20.0 mW = 0.020 W.
Convert the time from hours to seconds: 1 hr = 3600 s, so 1.00 hr = 3600 s.
Calculate the total energy emitted by the laser using the formula: Energy (E) = Power (P) \(\times\) Time (t).
Use the energy of a single photon formula: E_{photon} = \(\frac{E}{N}\), and relate it to wavelength using E_{photon} = \(\frac{hc}{\lambda}\), where h is Planck's constant and c is the speed of light, to solve for the wavelength \(\lambda\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
5m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Photon Energy

The energy of a photon is given by the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν (nu) is the frequency of the light. The frequency can be related to the wavelength (λ) using the equation c = λν, where c is the speed of light (approximately 3.00 x 10^8 m/s). Understanding photon energy is essential for calculating the wavelength from the number of emitted photons.
추천 영상:
가이드 코스
01:40
Photon Energy Formulas

Power and Energy Relationship

Power is defined as the rate at which energy is emitted or transferred. In this context, the laser's power output (20.0 mW) indicates how much energy is emitted per unit time. To find the total energy emitted over a specific time period, you can multiply the power by the time (in seconds). This relationship is crucial for determining the total energy associated with the emitted photons.
추천 영상:
가이드 코스
04:42
Power and Root Functions Example

Wavelength Calculation

Wavelength can be calculated using the relationship between energy and frequency. Once the total energy emitted by the laser is determined, the energy per photon can be found by dividing the total energy by the number of photons emitted. This energy can then be used to find the wavelength using the equation λ = hc/E, where E is the energy per photon. This process is key to solving the question regarding the wavelength of the laser light.
추천 영상:
가이드 코스
00:31
Frequency-Wavelength Relationship
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