The Relationship Between Energy and Wavelength in Electromagnetic Spectrum
What is the relationship between energy and wavelength in the electromagnetic spectrum?
Given the formula λ=hc/E, how is the maximum wavelength of light related to the energy required to remove electrons from the surface of a solid metal?
Explanation:
Energy and wavelength are inversely related in the electromagnetic spectrum. As stated in the problem, it takes 547 kJ to remove one mole of electrons from the atoms at the surface of a solid metal. The energy required for this process is directly related to the maximum wavelength of light capable of removing electrons.
According to the formula λ=hc/E, where λ represents wavelength, h is the Planck constant, c is the speed of light, and E is the energy required, we can calculate the maximum wavelength of light as follows:
λ = hc/E
λ = 6.626×10^-34 × 3×10^8 / 547×1000
λ = 36.3 × 10^-31 m
Therefore, the maximum wavelength of light capable of removing electrons from the surface of a solid metal is 36.3 × 10^-31 meters.
Details Explanation:
In the electromagnetic spectrum, energy and wavelength have an inverse relationship. This means that as the energy required to remove electrons increases, the wavelength of light capable of doing so decreases.
The formula λ=hc/E is used to determine the relationship between energy and wavelength in the spectrum. The Planck constant (h) and the speed of light (c) are constants in this formula, while E represents the energy required to remove electrons from the surface of a solid metal.
By substituting the given values into the formula, we can calculate the maximum wavelength of light required for the electron removal process. In this case, the energy of 547 kJ is used to determine the wavelength of 36.3 × 10^-31 meters.
Understanding this relationship is crucial in studying the behavior of electromagnetic waves and the interactions between light and matter. It also plays a significant role in various scientific fields, including optics, spectroscopy, and quantum mechanics.
For further information on the electromagnetic spectrum and its applications, you can explore related resources and educational materials.