These problems deal with the photoelectric effect, one of Einstein's great papers. Photons (light) below the threshold do not knock electrons loose from their atoms while photons above the threshold do knock them loose. The threshold is the break even point and represents the energy it takes to free the electron. Any additional energy beyond the threshold goes towards increasing the kinetic energy of the ejected electron.
We talk about the threshold frequency. For photons, the frequency is what determines the energy.
E is energy, h is Planck's constant, and n is frequency.
For part A, plug in the frequency given and Planck's constant and you will get the energy of a single photon at the threshold frequency, in joules.
Part B takes a few more steps. Here, they give us a wavelength. For light, the relationship between wavelength and frequency is always:
Ln = c
(wavelength x frequency = speed of light)
Think of a runner. His speed is dependent on how fast he can take a step (stride frequency) and how long those strides are (stride length or wavelength). The product of the two is the runners speed. The speed of light is a constant, so if we have frequency, we can always solve for wavelength. If we have wavelength, we can always solve for frequency.
Take the given wavelength (235 nm, or 235 x 10^-9 m) and convert to frequency. Is this frequency greater than the threshold from part A? If so, it will knock an electron loose and the amount of energy above the threshold becomes kinetic energy.
KE = hf-hf0
The kinetic energy (KE) is equal to the total energy (hf) minus the threshold energy (hf0). The f0 is the threshold frequency fro part A, f is the frequency from part B after converting from wavelength.
The threshold energy (hf0) represents the work it takes to break the electron free. Any surplus goes into moving the electron more energetically (kinetic energy)