(c) What wavelength of radiation has photons of energy 6.06 × 10^-19 J?

검증된 단계별 안내

Start by recalling the relationship between the energy of a photon and its wavelength, which is given by the equation: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy of the photon, \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) J·s), \( c \) is the speed of light (\( 3.00 \times 10^8 \) m/s), and \( \lambda \) is the wavelength.

Rearrange the equation to solve for wavelength \( \lambda \): \( \lambda = \frac{hc}{E} \).

Substitute the known values into the equation: \( h = 6.626 \times 10^{-34} \) J·s, \( c = 3.00 \times 10^8 \) m/s, and \( E = 6.06 \times 10^{-19} \) J.

Calculate the numerator \( hc \) by multiplying Planck's constant \( h \) by the speed of light \( c \).

Divide the result from the previous step by the energy \( E \) to find the wavelength \( \lambda \).

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주요 개념

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

Photon Energy

Photon energy is the energy carried by a single photon, which is a particle of light. It is directly proportional to the frequency of the radiation and inversely proportional to its wavelength. The energy of a photon can be calculated using the equation E = hν, where E is energy, h is Planck's constant (6.626 × 10^-34 J·s), and ν is the frequency of the radiation.

Wavelength and Frequency Relationship

The relationship between wavelength and frequency is described by the equation c = λν, where c is the speed of light (approximately 3.00 × 10^8 m/s), λ is the wavelength, and ν is the frequency. This equation shows that as the wavelength increases, the frequency decreases, and vice versa. Understanding this relationship is crucial for converting between energy, wavelength, and frequency.

Planck's Constant

Planck's constant is a fundamental constant in quantum mechanics, denoted as h, with a value of approximately 6.626 × 10^-34 J·s. It relates the energy of a photon to its frequency, serving as a bridge between the macroscopic and quantum worlds. This constant is essential for calculations involving photon energy and is a key component in the equations used to solve problems related to electromagnetic radiation.

(c) What wavelength of radiation has photons of energy 6.06 × 10-19 J?