# Homework Help: Photons of light emitted within the D-lines per second?

1. Nov 14, 2015

### moenste

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. Nov 14, 2015

### Staff: Mentor

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?

3. Nov 14, 2015

### moenste

(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.

4. Nov 14, 2015

### Staff: Mentor

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.

5. Nov 14, 2015

### moenste

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.

6. Nov 14, 2015

### Staff: Mentor

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)