The Physics
Hypertextbook
Opus in profectus

## Practice

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### 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 coulomb law constant (1/4πε0) and generate the planck units of…
1. charge
2. current
3. voltage
4. resistance
5. magnetic flux

#### solution

Fundamental constants 1 c can also be considered the Planck unit of speed. 2  is the quantum of angular momentum. 3 k ln 2 is the quantum of entropy.
quantity symbol value
speed of light1 c 3.00 × 108 m/s
gravitational constant G 6.67 × 10−11 N m2/kg2
reduced planck constant2 1.05 × 10−34 Js
boltzmann constant3 k 1.38 × 10−23 J/K
The original Planck units
quantity expression value
length √(ℏG/c3) 1.62 × 10−35 m
mass √(ℏc/G) 2.18 × 10−8 kg
time √(ℏG/c5) 5.39 × 10−44 s
temperature √(ℏc5/Gk2) 1.42 × 1032 K
quantity expression value
acceleration √(c7/ℏG) 5.56 × 1051 m/s2
force c4/G 1.21 × 1044 N
momentum √(ℏc3/G) 6.52 kg m/s
energy √(ℏc5/G) 1.96 × 109 J
power c5/G 3.63 × 1052 W
pressure c7/ℏG2  4.63 × 10113 Pa
density c5/ℏG2  5.16 × 1096 kg/m3
angular frequency √(c5/ℏG) 1.85 × 1043 rad/s
Extended Planck units for electricity and magnetism
quantity expression value
electrostatic constant 1/4πε0 8.99 × 109 Nm2/C2
charge √(4πε0c) 1.88 × 10−18 C
current √(4πε0c6/G) 3.48 × 1025 A
voltage √(c4/4πε0G) 1.04 × 1027 V
resistance 1/4πε0c 30.0 Ω
magnetic flux √(ℏ/4πε0c) 5.62 × 10−17 Wb