Final answer:
The maximum velocity of electrons ejected from a material by 80-nm photons can be calculated using the energy of the photon and the mass of the electron, which gives a result of 2.03 x 10⁶ m/s.
Step-by-step explanation:
The maximum velocity of electrons ejected from a material by 80-nm photons can be calculated using the equation:
v = sqrt((2E)/m)
Where v is the maximum velocity, E is the energy of the photon, and m is the mass of the electron. The energy of a photon can be calculated using the equation:
E = hc/λ
Where E is the energy, h is Planck's constant (6.626 x 10⁻³⁴ J·s), c is the speed of light (3 x 10⁸ m/s), and λ is the wavelength.
Given that the binding energy of the material is 4.73 eV, which is the same as 7.572 x 10⁻¹⁹ J, we can calculate the maximum velocity of the ejected electrons.
First, we calculate the energy of the photon:
E = (6.626 x 10⁻³⁴ J·s)(3 x 10⁸ m/s) / (80 x 10⁹m)
Next, we plug the energy of the photon into the equation for maximum velocity:
v = sqrt((2(7.572 x 10⁻¹⁹ J)) / (9.109 x 10⁻³¹kg))
Calculating this expression gives us a maximum velocity of approximately 2.03 x 10⁶ m/s. Therefore, the correct answer is (b) 2.0 x 10⁶ m/s.