How do I decide whether a photon of a specific light frequency will have enough energy to excite an electron?

You can use Rydberg's formula to determine the maximum wavelength of a photon
needed to raise the energy of an electron from one shell to another. The K shell is
energy level #1 (lower level) and the L shell is # 2 (upper level). The wavelength w
needed to excite the electron is found by the formula: 1/w = R(1/L² - 1/U²), where
L is the lower level (1 in this example), U is the upper level (2 in this example) and
R is the Rydberg constant, which for hydrogen is 10,967,758 waves per meter.
Substitute in known values and we get 1/w = 10967758(1 - ¼) = 8225818 waves/m.
Then w = 1.215 * 10**-7 meter, or 121.5 nanometers, which is ultraviolet light.
The wavelength of green light is between 400 and 450 nm, which is too long to
cause this excitation. You need a higher energy (shorter wavelength) photon.
Hope this helps!

The photon energy is given by: E=hf, where h is Planck's constant (=6.64e-34 Js) and f is the frequency. If this energy is >= the energy required to go from the K to L shell, then it will excite the electron