The work function for a certain metal is 3.00 eV. Calculate the speed of the electrons in m/s ejected by light of wavelength 209 nm. If it is not ejected, report a speed of 0.0.

Energy of incident light = Planck's constant*Frequency of incident light = hν = (hc/λ).

If (hc/λ) > Work Function,
The incident light has enough energy to eject an electron, and the kinetic energy is equal to the difference between (hc/λ) and the Work Function. The speed can be calculated from the kinetic energy (1/2*mv^2)

If (hc/λ) < Work Function,
There is not enough energy to eject the electron and the speed would be 0.0, as ejection would not occur.

To calculate the speed of the electrons ejected by light of a certain wavelength, we can use the equation:

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 (2.998 x 10^8 m/s), and λ is the wavelength of the light.

First, let's convert the wavelength from nanometers (nm) to meters (m):

λ = 209 nm = 209 x 10^-9 m = 2.09 x 10^-7 m

Now, we can calculate the energy of the photon using the equation above:

E = (6.626 x 10^-34 J*s) * (2.998 x 10^8 m/s) / (2.09 x 10^-7 m)
E ≈ 9.494 x 10^-19 J

Next, we can calculate the kinetic energy (KE) of the ejected electron using the equation:

KE = E - Work Function

KE = 9.494 x 10^-19 J - 3.00 eV

To convert eV to joules, we can use the conversion factor:

1 eV = 1.602 x 10^-19 J

So, the work function in joules is:

3.00 eV = 3.00 x 1.602 x 10^-19 J ≈ 4.806 x 10^-19 J

Substituting the values:

KE ≈ 9.494 x 10^-19 J - 4.806 x 10^-19 J ≈ 4.688 x 10^-19 J

Finally, we can calculate the speed of the ejected electron using the equation for kinetic energy:

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.

Rearranging the equation:

v^2 = (2KE)/m

v = √((2KE)/m)

Substituting the values:

v = √((2 * 4.688 x 10^-19 J) / 9.109 x 10^-31 kg)

v ≈ 2.321 x 10^6 m/s

Therefore, the speed of the electrons ejected by light of wavelength 209 nm is approximately 2.321 x 10^6 m/s.