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?

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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 \(\lambda\).

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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.

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.

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.

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?