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Photons of light emitted within the D-lines per second?

  1. Nov 14, 2015 #1
    1. The problem statement, all variables and given/known data
    (a) Calculate the energy of one photon of light emitted within the D-lines of a sodium lamp if the wavelength of the D-lines is 589 nm.

    (b) In a 200 W sodium street lamp, 30% of input electrical energy is emitted within the D-lines. How many photons of light are emitted within the D-lines per second?

    (h = 6.6 * 10-34 J s, c = 3 * 108 m s-1)

    Answers: (a) 3.4 * 10-19 J, (b) 1.8 * 1020 s-1

    2. The attempt at a solution
    (a) f = c / λ = 3 * 108 / 589 * 10-9 = 5.09 * 1014 Hz
    E = hf = 6.6 * 10-34 * 5.09 * 1014 = 3.4 * 10-19 J

    (b) No idea what to begin with. Any help please?
     
  2. jcsd
  3. Nov 14, 2015 #2

    mfb

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    If one apple has a mass of 200 g and I give you 2000 g of apples per second, how many apples per second do you get? How did you calculate that?
    What changes if you receive only 30% of the apples I give away?
     
  4. Nov 14, 2015 #3
    (i) I get 2,000 / 200 = 10 apples per second.

    (ii) It's either 2,000 * .3 = 600 g -> 600 / 200 = 3 apples per second or 10 * .3 = 3 apples per second.

    ---

    200 * 0.3 = 60 W
    60 * 3 * 108 = 1.8 * 1010 s-1

    But the answer is 1.8 * 1020 s-1.
     
  5. Nov 14, 2015 #4

    mfb

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    Missing units, but the result is right.
    The units are wrong, you multiply a power with a speed - the result cannot be a frequency.
    Why do you take the speed of light here? It is unrelated to this subquestion.

    In general, working with units helps to spot many errors.
     
  6. Nov 14, 2015 #5
    A lamp supplies 200 W of energy. 30% of this energy is emitted within the D-lines. It is 200 W * 0.3 = 60 W.

    Energy of one photon of light emitted within the D-lines = 3.4 * 10-19 J.

    60 W / 3.4 * 10-19 J = 1.8 * 1020 s-1.
     
  7. Nov 14, 2015 #6

    mfb

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    Correct.

    Just a notation issue: a/b * c is usually read as (a/b)*c which is not what you meant here.
    It is better to put brackets around the denominator: 60 W / (3.4 * 10-19 J)
     
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