$$ \begin{aligned} &\text { Calculate the mass of a photon of sodium light having wavelength }\\\ &5894 \AA \text { and velocity, } 3 \times 10^{8} \mathrm{~ms}^{-1}, h=6.6 \times 10^{-34} \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1} \end{aligned} $$

Planck's equation is a fundamental principle in the field of quantum mechanics that relates the energy of a photon to its frequency. The equation is denoted as \( E = hu \), where \( E \) represents the energy of the photon, \( h \) is Planck's constant, and \( u \) is the frequency of the photon.

The relationship states that the energy contained in a single photon is directly proportional to its frequency. Higher frequency photons (like those from gamma rays) contain more energy than lower frequency photons (like those from radio waves). To find the energy of a photon when you have the wavelength instead of frequency, you can use the modified form of Planck's equation that incorporates the speed of light \( c \), namely \( E = \frac{hc}{\lambda} \), where \( \lambda \) is the wavelength of the photon.

Applying this to the problem at hand, after converting the wavelength of sodium light from angstroms to meters, you would substitute the known values of Planck's constant and the speed of light into the equation to find the energy of the photon.

Einstein's mass-energy equivalence is a revolutionary concept from his theory of relativity, encapsulated in the famous equation \( E = mc^2 \). This equation describes how energy (\r( E \r)) and mass (\r( m \r)) are interrelated; essentially, mass can be converted into energy and vice versa, and the speed of light (\r( c \r)) squared is the conversion factor.

In the context of photons, which are massless particles when at rest, this relationship allows for calculating an 'effective mass' based on their energy when in motion. Although photons do not have rest mass, they do carry momentum and thus can be assigned a relativistic mass equivalent, derived from their energy as measured by Planck's equation. By rearranging Einstein's equation to solve for mass, \( m = \frac{E}{c^2} \), you can calculate this effective mass if you know the energy of the photon, which ties back to the energy calculated using Planck's equation.

Converting wavelengths is a crucial step in many physics calculations, particularly when working with light and other forms of electromagnetic radiation. Wavelength conversion typically involves changing the unit of measurement from one scale to another, such as from angstroms (\( \text{\rA} \)) to meters (m).

An angstrom is a unit of length that is commonly used to express the wavelengths of light and equals \( 10^{-10} \) meters. To convert a wavelength from angstroms to meters, you multiply the value by \( 10^{-10} \), enabling you to use SI units (meters) in further calculations like using Planck's equation. In the exercise, this step converts the sodium light wavelength from angstroms to meters before using it in subsequent calculations for energy and mass.

Attentiveness in unit conversion is vital for accuracy in scientific calculations. Even a small mistake in converting units can lead to significant errors in the final result. Therefore, understanding and correctly implementing wavelength conversion is essential when determining a photon's properties.