Questions: Which one of the following photons of electromagnetic radiation will have the greatest energy? One photon of red light (wavelength =650 nm) One photon of blue light (wavelength =470 nm) One photon of yellow light (wavelength =580 nm) One photon of green light (wavelength =550 nm) All of these will have the same energy.

Solution Steps

The energy of a photon is inversely proportional to its wavelength. This relationship is given by the equation:

\[ E = \frac{hc}{\lambda} \]

where:

• \(E\) is the energy of the photon,
• \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J}\cdot\text{s}\)),
• \(c\) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)),
• \(\lambda\) is the wavelength of the photon.

Given the wavelengths:

• Red light: \(650 \, \text{nm}\)
• Blue light: \(470 \, \text{nm}\)
• Yellow light: \(580 \, \text{nm}\)
• Green light: \(550 \, \text{nm}\)

Since energy is inversely proportional to wavelength, the photon with the shortest wavelength will have the greatest energy.

Among the given options, the blue light has the shortest wavelength of \(470 \, \text{nm}\).

Final Answer