Question

A laser produces 17.0 mW of light. In 4.00 hr , the laser emits 6.04×1020 photons. What is the wavelength of the laser?

Answer 1

The unit 'mW' means milliwatts. It is a unit of work. There are 1,000 milliwatts in a 1 Watt of work. In 4 hours, there are 14,400 seconds.

Work= Energy/time
17 mW * 1 W/1000 mW = Energy/(14,400 seconds)
Solving for energy,
Energy = 244.8 J
Energy/photon = 244.8 J/(6.04×10²⁰) = 4.053×10⁻¹⁹ J/photon

Using the Planck's equation:

E = hc/λ
where h = 6.626×10⁻³⁴ m²·kg/s, c = 3,00,000,000 m/s and λ is the wavelength

4.053×10⁻¹⁹ J/photon = (6.626×10⁻³⁴ m²·kg/s)(3,00,000,000 m/s)/λ
λ = 4.9×10⁻⁷ m or 49 micrometers

Answer 2

Answer:

λ = 490.81 nm

Explanation:

The first thing we need to do is use the correct units. Let's convert the mW to J/s.

1 Watt --------> 1 J/s

And we have 17 mW:

1 Watt --------> 1000 mW

Therefore, converting the mili watts to J/s we have:

17 mW * 1 J/s / 1000 mW = 0.017 J/s

Now, we have 4 hours, and in 1 hour we have 3600 seconds so:

t = 4 * 3600 = 14,400 s

Now, the expression to calculate the wavelength is the following:

E = hc/λ (1)

Where:

E: Energy emmited by the laser by photons (J)

h: Planck constant = 6.626x10⁻³⁴ J.s

c: speed of light = 3x10⁸ m/s

λ: wavelength (nm)

Now, we have the Power of the laser, but not the energy emmited by photons. Let's calculate that value:

E = 0.017 J/s * 14,400 s / 6.04x10²⁰

E = 4.05x10⁻¹⁹ J

Now that we have the value of Energy, we just solve for Lambda from (1) to get the wavelength:

λ = hc/E (2)

Now, all we have to do is replace the obtained values and solve for the wavelength:

λ = (6.626x10⁻³⁴ J.s * 3x10⁸ m/s) / 4.05x10⁻¹⁹ J

λ = 490.81x10⁻⁹ m

And to get this value to nanometers (The usual unit of wavelength):

1 m ------> 1x10⁹ nm

Therefore:

λ = 490.81 nm