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Photons are tiny particles of light that carry energy. To determine the energy of a photon, we use the formula: \( E = \frac{hc}{\lambda} \). Here, \( E \) is the energy, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength.

For example, to find the energy of a photon with a wavelength of 671 nm, we first convert the wavelength from nanometers to meters. In this case, 671 nm = 671 x 10^{-9} meters.

Substituting in the values: \( E = \frac{(6.626 \times 10^{-34}) \times (3 \times 10^8)}{671 \times 10^{-9}} \), we perform the calculation to get the energy of one photon, which is \( 2.96 \times 10^{-19} \) joules (J).

When discussing photon energy, Planck's constant \( (h) \) is a fundamental constant in physics that plays a key role. Its value is \( 6.626 \times 10^{-34} \) J·s.

Planck's constant is used to relate the energy of a photon to its frequency or wavelength. The formula \( E = h u \) (where \( u \) is frequency) or \( E = \frac{hc}{\lambda} \) shows this relationship.

Planck's constant is critical in quantum mechanics, as it signifies the smallest possible energy units (quanta) that can be emitted or absorbed as electromagnetic radiation.

Mass-energy equivalence is a concept in physics that shows how mass can be converted into energy and vice versa. This relationship is given by Einstein's famous equation: \( E = mc^2 \).

Here \( E \) is energy, \( m \) is mass, and \( c \) is the speed of light. This equation implies even a small amount of mass can be converted into a large amount of energy, because the speed of light \(( c \)) is a large number (approximately \( 3 \times 10^8 \) meters per second).

To find the mass equivalence of energy, we rearrange the equation to solve for mass: \( m = \frac{E}{c^2} \). Using this, if we know the energy, we can determine the corresponding mass.

Avogadro's number \( (N_A) \) is a fundamental constant in chemistry and physics that indicates the number of atoms, molecules, or particles in one mole of a substance. Its value is \( 6.022 \times 10^{23} \) particles per mole.

When dealing with photon energy, Avogadro's number helps us find the total energy in a mole of photons. For example, if one photon has an energy of \( 2.96 \times 10^{-19} \) J, the energy of one mole of these photons would be: \( 2.96 \times 10^{-19} \) J/photon \( \times 6.022 \times 10^{23} \) photons/mol = \( 1.78 \times 10^5 \) J/mol.

This is useful in fields like quantum chemistry and photochemistry, where reactions at the molecular level often involve calculations based on moles of photons.

Einstein's equation \( E = mc^2 \) is one of the most famous formulas in physics. It shows the relationship between energy \( (E) \) and mass \( (m) \) with a conversion factor \( c^2 \) (the speed of light squared).

This equation tells us that energy and mass are two forms of the same thing. Energy can be converted into mass and vice versa.

In practical terms, if we have the energy of a system or an object, we can find its equivalent mass. For example, the energy of one mole of photons ( \( 1.78 \times 10^5 \) J ) can be converted into mass: \( m = \frac{1.78 \times 10^5}{(3 \times 10^8)^2} = 1.98 \times 10^{-12} \) kg/mol. This shows the deep connection between mass and energy, and is foundational for understanding nuclear reactions and particle physics.