Final Answer:
The wavelength of the photo-ejected electrons is 0.0709 nm.
Step-by-step explanation:
The work function, Φ, of silver is 4.64 eV. Work function is the minimum energy required to remove an electron from the metal. When a sample of silver is bombarded with photons of wavelength 215 nm, the photo-electrons are ejected from the metal. The energy of each photon is given by the equation: E = hc/λ, where h is Planck's constant (6.626 x 10^-34 Js), c is the speed of light (2.998 x 10^8 m/s) and λ is the wavelength of the photon. Substituting the given values in the equation, we get the energy of each photon as 3.48 x 10^-19 J.
As per the law of conservation of energy, the energy of the photon must be equal to the work function of the silver plus the kinetic energy of the photo-ejected electrons. This is given by the equation: K.E. = 3.48 x 10^-19 J - 4.64 eV. Converting the electron volts to joules, we get the kinetic energy of the photo-ejected electrons as 8.78 x 10^-19 J. Kinetic energy of the electrons is given by the equation: K.E. = ½ mv², where m is the mass of the electron (9.109 x 10^-31 kg) and v is the velocity of the electron. Substituting the given values in the equation, we get the velocity of the electron as 8.14 x 10^7 m/s.
Using the equation: λ = c/v, where c is the speed of light (2.998 x 10^8 m/s) and v is the velocity of the electron, we get the wavelength of the photo-ejected electrons as 0.0709 nm.
Therefore, the wavelength of the photo-ejected electrons is 0.0709 nm.