To find the threshold frequency, you can use the equation E = hf, where E is the energy (in electron volts, eV), h is Planck's constant (4.1357 × 10^-15 eV·s), and f is the frequency (in hertz, Hz).
Since the work function is given in eV, you can convert it to joules by multiplying it by the conversion factor 1.6022 × 10^-19. This gives a work function of 5.33 × 10^-19 J.
To find the threshold frequency, you need to first calculate the energy required to overcome the work function. This can be done by subtracting the work function from the energy of an electron, which is 0.511 MeV (million electron volts).
So, the energy required would be 0.511 MeV - 3.33 eV = 0.50767 MeV.
Now, you can plug this energy into the equation E = hf and solve for f.
0.50767 MeV = (4.1357 × 10^-15 eV·s) f
Solving for f, you get a threshold frequency of 1.226 × 10^21 Hz.
To find the minimum frequency, you can simply divide the threshold frequency by 2π, as the minimum frequency is equal to the threshold frequency divided by 2π.
So, the minimum frequency would be 1.226 × 10^21 Hz / 2π = 1.951 × 10^20 Hz.
In summary, to find the threshold frequency when the work function is 3.33eV, you would first convert the work function to joules, subtract it from the energy of an electron, and then solve for the frequency using the equation E = hf. This would give you a threshold frequency of 1.226 × 10^21 Hz. The minimum frequency can be found by dividing the threshold frequency by 2π, giving a value of 1.951 × 10^20 Hz.
