Final answer:
a) The longest wavelength of light that can cause emission of electrons from the metal is approximately 1006 nm. b) The energy of the ejected electrons when light of 740 nm shines on the metal is approximately 2.67 eV.
Step-by-step explanation:
a) The longest wavelength of light that can cause emission of electrons can be determined using the equation: λ = hc/E, where λ is the wavelength, h is Planck's constant (6.63 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and E is the work function. Plugging in the values, we get λ = (6.63 x 10^-34 J·s)(3.00 x 10^8 m/s) / (1.24 eV). After converting 1.24 eV to joules (1 eV = 1.602 x 10^-19 J), we can calculate the longest wavelength to be approximately 1006 nm.
b) To find the energy of the ejected electrons when light of 740 nm shines on the metal, we can use the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. Substituting the given values, we get E = (6.63 x 10^-34 J·s)(3.00 x 10^8 m/s) / (740 x 10^-9 m). The energy of the ejected electrons is approximately 2.67 eV.