Question

Which is greater, the energy of one photon of orange light or the energy of one quantum of radiation having a wavelength of 4.26 x 10"m? Show your work.

Answer 1

Answer: The energy of one quantum of radiation having a wavelength of
`\(4.26 * 10^(-9)\)` meters is greater than the energy of one photon of orange light.

Step-by-step explanation:

The energy of a photon or a quantum of radiation can be calculated using the formula:

E = hc/λ

where:

- E is the energy of the photon,

- h is Planck's constant (6.626 x 10^-34 J*s),

- c is the speed of light (3.0 x 10^8 m/s), and

- λ is the wavelength of the light.

The wavelength of orange light is typically around 600 nm (or 600 x 10^-9 m).

The energy of a photon of orange light, which has a wavelength of approximately 600 nm, is approximately
`\(3.311 * 10^(-19)\)` Joules or 2.066 electronvolts (eV).

The energy of a quantum of radiation with a wavelength of
`\(4.26 * 10^(-9)\)` meters is approximately
`\(4.663 * 10^(-17)\)` Joules or 29.1 electronvolts (eV).

Answer 2

To compare the energy of one photon of orange light and one quantum of radiation with a given wavelength, we can use the equation:

E = hc / λ

Where:
E is the energy of the photon or quantum
h is Planck's constant (6.62607015 × 10^-34 J·s)
c is the speed of light (approximately 3.0 × 10^8 m/s)
λ is the wavelength of the radiation

Let's calculate the energy for each case:

For the photon of orange light, we need to determine its wavelength. The wavelength of orange light typically ranges from approximately 590 nm to 620 nm. Let's assume a wavelength of 605 nm (6.05 × 10^-7 m) for our calculation.

E_orange = (6.62607015 × 10^-34 J·s * 3.0 × 10^8 m/s) / (6.05 × 10^-7 m)
E_orange ≈ 3.31 × 10^-19 J

For the quantum of radiation with a given wavelength of 4.26 × 10^-6 m:

E_radiation = (6.62607015 × 10^-34 J·s * 3.0 × 10^8 m/s) / (4.26 × 10^-6 m)
E_radiation ≈ 4.90 × 10^-19 J

Comparing the two energies, we find that the energy of one quantum of radiation with a wavelength of 4.26 × 10^-6 m is greater than the energy of one photon of orange light.