How is a shorter wavelength photon related to frequency, energy, and ionizing potential?

How is a shorter wavelength photon related to frequency, energy, and ionizing potential?

• A. Shorter wavelength = lower frequency, lower energy, decreased ionization potential
• B. Shorter wavelength = higher frequency, higher energy, increased ionization potential
• C. Shorter wavelength = constant frequency, energy, and ionizing potential
• D. Shorter wavelength = fluctuating frequency, energy, and ionizing potential

Answer: (B)

A shorter wavelength photon is indeed related to higher frequency, higher energy, and increased ionizing potential. This is grounded in the fundamental relationships in physics, specifically governed by the equations of electromagnetic radiation.

The relationship between wavelength and frequency is described by the equation:

[ c = \lambda \cdot f ]

where ( c ) is the speed of light, ( \lambda ) is the wavelength, and ( f ) is the frequency. From this equation, it is clear that a decrease in wavelength (( \lambda )) results in an increase in frequency (( f )), given that the speed of light remains constant.

Additionally, energy (( E )) of a photon is determined by the equation:

[ E = h \cdot f ]

where ( h ) is Planck's constant. As the frequency increases (due to the shorter wavelength), the energy of the photon correspondingly increases. This illustrates that shorter wavelengths not only lead to higher frequencies but also directly result in higher energy values.

Moreover, ions can be produced when photons have sufficient energy to ionize atoms, which means that a higher energy photon (associated with a shorter wavelength) has a greater potential for ionization. Therefore, as the