A stellar object is emitting radiation at 3.55 mm. a. What type of electromagnetic spectrum is this radiation? b. If a detector is capturing 3.2×108 photons per second at this wavelength, what is the total energy of the photons detected in 1.0 hour?

검증된 단계별 안내

Identify the type of electromagnetic spectrum by comparing the given wavelength (3.55 mm) to the electromagnetic spectrum chart. Millimeter wavelengths typically fall within the microwave region.

To find the energy of a single photon, use the formula: \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant (6.626 \(\times\) 10^{-34} \(\text{ J s}\)), \( c \) is the speed of light (3.00 \(\times\) 10^8 \(\text{ m/s}\)), and \( \lambda \) is the wavelength in meters (3.55 mm = 3.55 \(\times\) 10^{-3} \(\text{ m}\)).

Calculate the energy of a single photon using the formula from step 2.

Determine the total number of photons detected in 1.0 hour by multiplying the rate of photon detection (3.2 \(\times\) 10^8 photons/second) by the number of seconds in an hour (3600 seconds).

Calculate the total energy of the photons detected in 1.0 hour by multiplying the energy of a single photon (from step 3) by the total number of photons (from step 4).

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

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

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, which vary in wavelength and frequency. Radiation at 3.55 mm falls within the microwave region of the spectrum, which is characterized by longer wavelengths than infrared radiation but shorter than radio waves. Understanding the position of radiation within the spectrum is crucial for identifying its properties and applications.

Photon Energy

Photons are particles of light that carry energy, which can be calculated using the equation E = hf, where E is energy, h is Planck's constant, and f is the frequency of the radiation. The frequency can be derived from the wavelength using the speed of light equation, c = λf. This relationship is essential for determining the energy of the photons emitted by the stellar object.

Energy Calculation Over Time

To find the total energy of photons detected over a specific time period, one must first calculate the energy of a single photon and then multiply it by the number of photons detected per second and the total time in seconds. In this case, with 3.2×10^8 photons detected per second over 1 hour (3600 seconds), the total energy can be computed, illustrating the relationship between time, photon count, and energy.