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I'm a bit confused here... when it says an atom can continually absorb light, does this mean that you can keep feeding it energy until it escapes from the metal? I'm assuming you can do this...

okay so the atom is 0.1 m away from the light source, so if you draw straight lines from the point source to the top and bottom of the atom, you get an isoceles triangle, two of the lengths which are (very close to) 0.1 m and the base which is just the diametre of the atom, 2 angstroms. Now, since the angle theta, which we define to be the vertex angle of this isoceles triangle, is extremely small, we can approximate it by saying

0.1 * sin theta = 2 e - 10

0.1 * theta = 2 e - 10

theta = 2 e - 9 rad

Now, this means that the atom receives

2e-9 / (2 pi) * 25 joules/sec of energy.

But a total of 4 eV is needed, so we have that the total time taken would be 2.01 e -11 sec.