a) To calculate the minimum frequency of electromagnetic radiation required to release electrons from the metal, you can use the following formula:
f = W / h
where f is the minimum frequency of electromagnetic radiation required, W is the work function of the metal in joules, and h is the Planck constant in joules per second.
Plugging in the values for W and h, you get:
f = (5.86 x 10^-19 J) / (6.626 x 10^-34 J/s) = 8.9 x 10^14 Hz
This is the minimum frequency of electromagnetic radiation required to release electrons from the magnesium metal.
b) To calculate the kinetic energy of the ejected electronic light of frequency 2.00 x 10^14 Hz, you can use the following formula:
KE = hf - W
where KE is the kinetic energy of the ejected electron, h is the Planck constant in joules per second, f is the frequency of the electromagnetic radiation in hertz, and W is the work function of the metal in joules.
Plugging in the values for h, f, and W, you get:
KE = (6.626 x 10^-34 J/s) * (2.00 x 10^14 Hz) - (5.86 x 10^-19 J) = 1.32 x 10^-19 J - 5.86 x 10^-19 J = -4.54 x 10^-20 J
This is the kinetic energy of the ejected electron when light of frequency 2.00 x 10^14 Hz is used to irradiate the magnesium metal. Since the kinetic energy is negative, this means that the electron is not released from the metal when irradiated with this frequency. The frequency of the electromagnetic radiation needs to be higher than the minimum frequency required to release the electron in order for the electron to be ejected from the metal.