Fermi Problems Examples 1 Solutions
Magee Knowledge Society
1 What is the total sum height of everyone on the Earth, in centimeters?
Human population: 7 × 109 Average height: 150 cm
Total height: 7 × 109 *1.5 × 102 =1.05 × 1012 cm
2 What is the total body mass, in grams, of all the students at Magee?
Student population: 1 × 103 Average Mass: 50 kg=5 × 104 g
Total mass: 1 × 103 *5 × 104 =5 × 107 g
3 What is 264 ?
See section 2 of notes for explanation.
log 264
=64 log 2
=64 ∗ 0.3
=19.2
1019.2
=1019 ∗ 100.2
=1.58 × 1019
Actual answer: 1.84 × 1019
4 What is the kinetic energy of the Earth as it orbits the sun in Joules? (Disregard rotational
energy from the spinning of the Earth on its axis).
Distance from Earth to Sun, AU: 1.5 × 1011 m Mass of Earth: 5.98 × 1024 kg Seconds in
year: 3 × 107 s
d
t
2πr
=
t
2 ∗ 3 ∗ 1.5 × 1011
=
3 × 107
m
= 3 × 104
s
mv 2
E=
2
1
2
= ∗ 6 × 1024 ∗ 3 × 104
2
= 27 × 1032
v=
= 2.7 × 1033 J
5 What is the mass, in grams, of a single water molecule?
Atomic Mass Unit: 1.67 × 10−27 kg=1.67 × 10−24 g
1
Oxygen: 16ATU
Hydrogen: 1ATU
Water: 18ATU = 2.8 × 10−23 g
Without approximation: 3.0 × 10−23 g
This can also be solved by recalling that a mole of water is 18grams, and has 6.022 × 1023
molecules in it.
6 What is the ratio between the electric force and gravitational force between the proton and
electron of a hydrogen atom?
Mass of proton: 1.67 × 10−27 kg Mass of electron: 9.11 × 10−31 kg
Elementary charge: 1.60 × 10−19 C
2
k=9 × 109 NCm2
2
G=6.67 × 10−11 Nkgm2
q1 q2
r2
m1 m2
Fg = G 2
r
Fe
Fg
kq1 q2
=
Gm1 m2
9 × 109 ∗ 1.6 × 10−19 ∗ 1.6 × 10−19
=
6.67 × 10−11 ∗ 9.11 × 10−31 ∗ 1.67 × 10−27
∗ 1.6
9 ∗
1.6
40
= ∗
∗ 10
6.67 ∗ 9.11
1.67
=2.2 × 1039
Fe = k
Answer according to Giancoli: 2.3 × 1039
2