To determine the speed of electrons ejected by radiation of a specific wavelength, we can use the equation for the energy of a photon:
E = hc/λ
where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J*s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the radiation.
First, let's calculate the energy of the radiation with a wavelength of 265 nm (nanometers):
E = (6.626 x 10^-34 J*s * 3.00 x 10^8 m/s) / (265 x 10^-9 m) E ≈ 7.50 x 10^-19 J
Now, we need to find the kinetic energy (KE) of the ejected electrons. The work function (Φ) of the metal surface represents the minimum energy required to remove an electron from the metal. The remaining energy of the photon (E - Φ) will be converted into the kinetic energy of the electron.
Let's assume the work function of the metal surface is zero (Φ = 0) for simplicity. In this case, the entire energy of the photon will go into the kinetic energy of the electron:
KE = E = 7.50 x 10^-19 J
The speed of the ejected electron can be determined using the equation:
KE = (1/2)mv^2
where m is the mass of the electron (9.109 x 10^-31 kg) and v is the speed of the electron.
Let's rearrange the equation to solve for v:
v = sqrt((2KE) / m)
v = sqrt((2 * 7.50 x 10^-19 J) / 9.109 x 10^-31 kg) v ≈ 1.45 x 10^6 m/s
Therefore, when ultraviolet radiation with a wavelength of 265 nm strikes the metal surface, the electrons are ejected with a speed of approximately 1.45 x 10^6 m/s.