Show that the photons in a 1240 -nm infrared beam have...

Show that the photons in a 1240 -nm infrared beam have energies of $1.00 \mathrm{eV}$ $$ \mathrm{E}=h f=\frac{h \mathrm{c}}{\lambda}=\frac{\left(6.63 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\right)\left(2.998 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)}{1240 \times 10^{-9} \mathrm{~m}}=1.602 \times 10^{-19} \mathrm{~J}=1.00 \mathrm{eV} $$

Show that the photons in a 1240 -nm infrared beam have energies of $1.00 \mathrm{eV}$
$$
\mathrm{E}=h f=\frac{h \mathrm{c}}{\lambda}=\frac{\left(6.63 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\right)\left(2.998 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)}{1240 \times 10^{-9} \mathrm{~m}}=1.602 \times 10^{-19} \mathrm{~J}=1.00 \mathrm{eV}
$$

Key Concepts

Energy Unit Conversion

Energy unit conversion, such as converting from joules to electron volts, is essential in many applications in physics. The electron volt is a convenient unit of energy at the atomic and subatomic scales, and converting between these units helps in comparing and understanding energy magnitudes in different contexts.

Photon Energy

The energy of a photon is determined by the relationship E = hf or equivalently E = hc/?, linking the energy directly with the photon's frequency or inversely with its wavelength. This relationship underscores the particle-like behavior of photons and the quantization of electromagnetic energy.

Photon

Photons are the fundamental quanta of light and electromagnetic radiation, carrying energy that is quantized in discrete packets. They are massless particles characterized by their frequency and wavelength, and they follow the principles of quantum mechanics.

Planck's Constant

Planck's constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It serves as the proportionality factor in the equation E = hf, indicating that energy is quantized in units defined by this constant.

Speed of Light

The speed of light is a universal constant that represents the speed at which light propagates through a vacuum. It plays a critical role in the relationship between a photon's wavelength and frequency, as evident in the equation c = ?f.

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