Final answer:
The wavelength of the incident photon is calculated using the kinetic energy of the ejected electron and the threshold frequency of the metal, applying the principles of photoelectric effect.
Step-by-step explanation:
To find the wavelength of the incident photon that caused the ejection of an electron with a certain velocity, we can use the principles of the photoelectric effect, which is a phenomenon well studied in physics. Since the electron is ejected with a velocity of 6.70 x 10⁵ m/s, we can use the kinetic energy of the electron to determine the energy of the incident photon. The energy of the photon (E) is given by the sum of the work function (φ), which is the energy needed to eject an electron from the metal, and the kinetic energy (KE) of the ejected electron (E = φ + KE).
The work function can be calculated using the threshold frequency (ν0) provided by the equation φ = hν0, where h is Planck's constant (6.63 x 10³⁴ J⋅s). Once the work function and the kinetic energy of the electron (KE = ½mv²) are known, we can find the energy of the incident photon. Finally, the wavelength (λ) of the photon can be calculated using the equation E = hc/λ, where c is the speed of light.