A photon has momentum of magnitude 8.24 * 10-28 kg # m>s. (b) What is the wavelength of this photon? In what region of the electromagnetic spectrum does it lie?

Verified step by step guidance

1. Calculate the wavelength of the photon using the formula for the momentum of a photon, which is given by \( p = \frac{h}{\lambda} \), where \( p \) is the momentum, \( h \) is Planck's constant (approximately \( 6.626 \times 10^{-34} \) Js), and \( \lambda \) is the wavelength. Rearrange the formula to solve for \( \lambda \): \( \lambda = \frac{h}{p} \).
2. Substitute the values of \( p \) and \( h \) into the rearranged formula to find the wavelength \( \lambda \).
3. Identify the region of the electromagnetic spectrum the wavelength belongs to by comparing the calculated wavelength to the typical ranges for different regions (radio, microwave, infrared, visible, ultraviolet, X-rays, gamma rays).
4. Determine if the wavelength falls within the range of visible light (approximately 400 nm to 700 nm) or another region of the spectrum.
5. Conclude in which specific region of the electromagnetic spectrum the photon's wavelength lies based on the comparison.

Key Concepts

Photon Momentum

Photons, despite having no mass, carry momentum, which is given by the formula p = E/c, where p is momentum, E is energy, and c is the speed of light. The momentum of a photon can also be expressed in terms of its wavelength using the relation p = h/λ, where h is Planck's constant and λ is the wavelength. This relationship is crucial for determining the wavelength of a photon when its momentum is known.

Planck's Constant

Planck's constant (h) is a fundamental constant in quantum mechanics, approximately equal to 6.626 x 10^-34 Js. It relates the energy of a photon to its frequency through the equation E = hν, where ν is the frequency. In the context of photon momentum, it is used to connect momentum and wavelength, making it essential for solving problems involving photons.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from radio waves to gamma rays. Each type of radiation is characterized by its wavelength or frequency. Understanding where a photon lies within this spectrum is important for applications in fields such as telecommunications, medicine, and astronomy, as different regions have distinct properties and uses.