A photon has momentum of magnitude $8.24 \times 10^{- 28}$ kg-m/s. What is the energy of this photon? Give your answer in joules and in electron volts.

검증된 단계별 안내

Step 1: Recall the relationship between the energy $E$ of a photon and its momentum $p$. The formula is $E = pc$, where $c$ is the speed of light in a vacuum ($c = 3.00 \times 10^8\, \text{m/s}$).

Step 2: Substitute the given momentum $p = 8.24 \times 10^{-28}\, \text{kg·m/s}$ and the speed of light $c = 3.00 \times 10^8\, \text{m/s}$ into the formula $E = pc$. This will give the energy in joules.

Step 3: To convert the energy from joules to electron volts (eV), use the conversion factor $1\, \text{eV} = 1.602 \times 10^{-19}\, \text{J}$. Divide the energy in joules by this factor to find the energy in electron volts.

Step 4: Ensure that the units are consistent throughout the calculation. Verify that the energy in joules and electron volts are correctly calculated and match the expected order of magnitude.

Step 5: Present the final energy values in both joules and electron volts, ensuring proper significant figures based on the given data.

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주요 개념

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Photon Momentum

Photons, which are particles of light, possess momentum despite having no mass. The momentum of a photon is given by the equation p = E/c, where p is momentum, E is energy, and c is the speed of light in a vacuum. This relationship highlights the wave-particle duality of light, where photons exhibit both wave-like and particle-like properties.

Energy of a Photon

The energy of a photon can be calculated using the equation E = hf, where E is energy, h is Planck's constant (approximately 6.626 x 10^-34 J·s), and f is the frequency of the photon. Alternatively, energy can also be expressed in terms of momentum using E = pc, linking the concepts of energy and momentum for massless particles like photons.

Conversion Between Joules and Electron Volts

Energy can be expressed in different units, with joules (J) and electron volts (eV) being common in physics. One electron volt is defined as the energy gained by an electron when it is accelerated through a potential difference of one volt, equivalent to approximately 1.602 x 10^-19 joules. Understanding how to convert between these units is essential for accurately reporting energy values in various contexts.