Photoelectric Effect and the human eye

[daveyman]

Homework Statement

Under favorable circumstances the human eye can detect 1.0e-18 J of electromagnetic energy. How many 600-nm photons does this represent?
(Modern Physics, Arthur Beiser, 6th Edition, Pg. 89)

Homework Equations

My answer is unreasonably low. My mistake is probably very simple, but I'm not sure what it is. Any ideas?

The Attempt at a Solution

First, I attempted to find the energy in a single photon with a wavelength of 600nm.
Since E=hf, I simply multiplied h and f.
I found f by the relationship f=c/lambda.
So, (6.626e-34)(3e8)/(600e-9) = 3.313e-19

Then, I just divided the total amount of energy by this amount (the amount of energy in a single proton).

(1.0e-18)(3.313e-19) = 3.02

I'm guessing that the eye can detect more than 3 photons at a time :-) but I'm not sure what I'm doing wrong. Help!

 

[G01]

Yes, the eye can detect more than three photons at a time, but, according to this problem, apparently it can't detect less than 3 photons at a time. You are finding the minimum amount of 600nm photons the eye can detect, by utilizing the minimum energy the eye can detect.

Your work looks fine to me.

 

[daveyman]

Thanks for the quick response! I'm glad to hear that my work makes sense, but how did you come to the conclusion that the given energy is a minimum? The way it is worded ("under favorable circumstances") it almost sounds like it would be maximum...

 

[G01]

I interpreted "under favorable circumstances" as "maximum performance of the eye" i.e. the smallest amount of light the eye can detect will be less and less as it performs better.

So, I interpret the result as:

"Under favorable circumstances, i.e. when your eyes are performing at their very best, they can distinguish at least three photons at a time, but no less.

Also, we know for a fact that the eye can detect more than that amount of energy, so it can't be a maximum.

 

[daveyman]

Oh! - the performance of the eye here is based on how little light the eye can still distinguish - I totally get it! That makes tons of sense, actually - thanks!

 

[G01]

No problem.