A radiation with frequency 8.5×10^14Hz is incident on a metal emitting photo electrons. Taking Planck's constant, determine the threshold wavelength.
To determine the threshold wavelength, we need to use the concept of the photoelectric effect and Planck's constant.
The photoelectric effect explains how metals emit electrons when light of a certain frequency is incident upon them. The threshold frequency (or threshold wavelength) is the minimum frequency (or maximum wavelength) of light required to remove electrons from the metal's surface.
Planck's constant, denoted by h, is a fundamental constant in quantum physics. It relates the energy of a photon to its frequency through the equation E = hf, where E is the energy, h is Planck's constant, and f is the frequency of the radiation.
To calculate the threshold wavelength, we can use the equation for the energy of a photon, E = hc/λ, where c is the speed of light and λ is the wavelength of the radiation.
Here's how we can solve for the threshold wavelength:
1. Convert the frequency to Hz: 8.5×10^14Hz.
2. Substitute the values into the equation E = hc/λ and solve for λ:
E = hf
hc/λ = hf
λ = hc / f
3. Substitute the values of Planck's constant and the frequency into the equation:
λ = (6.63 × 10^-34 J·s) / (8.5 × 10^14 Hz)
4. Calculate the threshold wavelength:
λ ≈ 7.79 × 10^-7 meters
Therefore, the threshold wavelength is approximately 7.79 × 10^-7 meters.