Calculate the energy of a photon of electromagnetic radiation at each of the frequencies indicated in Problem 40. a. 100.2 MHz (typical frequency for FM radio broadcasting) b. 1070 kHz (typical frequency for AM radio broadcasting) (assume four significant figures) c. 835.6 MHz (common frequency used for cell phone communication)

검증된 단계별 안내

Identify the formula to calculate the energy of a photon: \( E = h \cdot f \), where \( E \) is the energy, \( h \) is Planck's constant \( 6.626 \times 10^{-34} \text{ J} \cdot \text{s} \), and \( f \) is the frequency.

Convert the given frequencies to hertz (Hz) if necessary: a. 100.2 MHz = 100.2 \(\times\) 10^6 \(\text{ Hz}\), b. 1070 kHz = 1070 \(\times\) 10^3 \(\text{ Hz}\), c. 835.6 MHz = 835.6 \(\times\) 10^6 \(\text{ Hz}\).

Substitute the frequency values into the energy formula for each case: a. \( E = 6.626 \times 10^{-34} \text{ J} \cdot \text{s} \times 100.2 \times 10^6 \text{ Hz} \), b. \( E = 6.626 \times 10^{-34} \text{ J} \cdot \text{s} \times 1070 \times 10^3 \text{ Hz} \), c. \( E = 6.626 \times 10^{-34} \text{ J} \cdot \text{s} \times 835.6 \times 10^6 \text{ Hz} \).

Calculate the energy for each frequency using the formula and ensure the result is expressed with four significant figures.

Review the calculated energies to ensure they are reasonable and consistent with the expected range for electromagnetic radiation energies.

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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 directly proportional to its frequency, described 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 in hertz. This relationship indicates that higher frequency photons carry more energy, which is crucial for understanding electromagnetic radiation.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from radio waves to gamma rays. Frequencies mentioned in the question, such as MHz and kHz, fall within the radio wave region of the spectrum, which is used for various communication technologies, including FM and AM radio broadcasting.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. When performing calculations, especially in scientific contexts, it is essential to maintain the correct number of significant figures to ensure accuracy and reliability in the results, as indicated in the problem's instruction to assume four significant figures.