The Physics
Hypertextbook
Opus in profectus

## Practice

### practice problem 1

A laser used in a fiber optic communication system operates at a wavelength of 635 nm, has a power output of 1 mW, and can transmit data at a rate of 2.5 gigabits per second. Compute the following quantities…
1. the frequency of the electromagnetic radiation
2. the color of the electromagnetic radiation
3. the duration of a single pulse
4. the length of a single pulse
5. the number of wavelengths in a single pulse
6. the energy of a single pulse
7. the energy of a single photon
8. the number of photons in a single pulse

#### solution

Here are the solutions.

1. Use the wavelength given and the speed of light to determine the frequency of the electromagnetic radiation.

 f = c λ
⇐  c = fλ
 f = 3.00 × 108 m/s 635 × 10−9 m
 f = 4.72 × 1014 Hz or 472 THz
2. Use your favorite reference source to determine the color of the electromagnetic radiation. You can use either the wavelength or the frequency to do this, depending on the way your source is organized. Color is subjective, so more than one answer is possible. Red or orange are the most reasonable answers.

3. The duration of a single pulse is determined by the frequency at which information is sent. Digital information consists of ones and zeros only. The laser encodes this by either remaining in its current state (zero) or changing to a different state (one). The shortest pulse would occur when the laser was off, and then sent a pair of ones down the fiber. This would switch the laser on then off just as fast as possible — the reciprocal of the data transfer rate fdata. (Sometimes the symbol r is used for this quantity.) Basically, use the fact that period is the inverse of frequency.

 T = 1 fdata
 T = 1 2.5 × 109 Hz
 T = 4.00 × 10−10 s or 0.400 ns
4. Use the definition of speed to determine the length of a single pulse.

ℓ = cT  ⇐
 v = Δs Δt
 ℓ = (3.00 × 108 m/s)(4.00 × 10−10 s)
 ℓ = 0.120 m
5. Dividing the wavelength into the pulse length will give you the number of wavelengths in a single pulse. I see no reason to be overly precise here, so I'm going to report this answer with only two significant digits.

 n = ℓ λ
 n = 0.120 m 635 × 10−9 m
 n = 190,000 wavelengths
6. Use the definition of power to determine the energy of a single pulse.

Epulse = Pt  ⇐
 P = W t
 Epulse = (0.001 W)(4.00 × 10−10 s)
 Epulse = 4.00 × 10−13 J
7. Use Planck's equation to determine the energy of a single photon.

 Ephoton = hfEphoton = (6.63 × 10− J s)(4.72 × 1014 Hz)Ephoton = 3.13 × 10−19 J
8. Dividing the energy of one photon into the energy of one pulse will give you the number of photons in a single pulse. Again, I see no reason for unnecessary precision here. Two significant digits are enough.

 n = Epulse Ephoton
 n = 4.00 × 10−13 J 3.13 × 10−19 J
 n = 1,300,000 photons

This answer is not the same as the number of wavelengths in a pulse because wavelength is not the length of a photon. As far as anyone knows, photons have no physical size.

Write something.

Write something.

### practice problem 4

Combine the speed of light (c), gravitational constant (G), and the reduced Planck constant (ℏ) so as to generate the Planck units of…
1. length
2. mass
3. time
Add boltzmann constant (k) to the list and generate the Planck unit of…
1. temperature
Combine your results and generate the Planck units of…
1. acceleration
2. force
3. momentum
4. energy
5. power
6. pressure
7. density
8. angular frequency
Include the constant from Coulomb's law (1/4πε0) and generate the Planck units of…
1. charge
2. current
3. voltage
4. resistance
5. magnetic flux

#### solution

The solutions to this practice problem can be found in the discussion section of this topic.