Question

Use the orders of magnitude you found in the previous problem to answer the following questions to within an order of magnitude.

(a) How many electrons would it take to equal the mass of a proton?
a) 10^3
b) 10^6
c) 10^9
d) 10^12

(b) How many Earths would it take to equal the mass of the Sun?
a) 10^4
b) 10^5
c) 10^6
d) 10^7

(c) How many Earth–Moon distances would it take to cover the distance from Earth to the Sun?
a) 10^2
b) 10^3
c) 10^4
d) 10^5

(d) How many Moon atmospheres would it take to equal the mass of Earth’s atmosphere?
a) 10^11
b) 10^12
c) 10^13
d) 10^14

(e) How many moons would it take to equal the mass of Earth?
a) 10^2
b) 10^3
c) 10^4
d) 10^5

(f) How many protons would it take to equal the mass of the Sun?
a) 10^53
b) 10^54
c) 10^55
d) 10^56

Answer 1

To equal the mass of a proton, it would take approximately 10^27 electrons. It would take approximately 10^6 Earths to equal the mass of the Sun. To cover the distance from Earth to the Sun, it would take approximately 10^2 Earth-Moon distances. It would take approximately 10^12 Moon atmospheres to equal the mass of Earth's atmosphere. And finally, it would take approximately 10^2 moons to equal the mass of Earth.

Step-by-step explanation:

To answer these questions within an order of magnitude, we can use the information provided in problem 14. The mass of a proton is given as 1.67 × 10-27 kg. So, to equal the mass of a proton, we would need approximately 1027 electrons.

The mass of the Sun is given as 1.99 × 1030 kg. The mass of the Earth is given as 5.97 × 1024 kg. Therefore, it would take approximately 106 Earths to equal the mass of the Sun.

The distance from Earth to the Sun is approximately 1.5 × 1011 m. The Earth-Moon distance is given as 3.84 × 108 m. So, it would take approximately 102 Earth-Moon distances to cover the distance from Earth to the Sun.

The mass of Earth's atmosphere is given as 5.1 × 1018 kg. The mass of the Moon's atmosphere is given as 2.5 × 104 kg. Therefore, it would take approximately 1012 Moon atmospheres to equal the mass of Earth's atmosphere.

Lastly, the mass of Earth is given as 5.97 × 1024 kg. The mass of the Moon is given as 7.34 × 1022 kg. So, it would take approximately 102 moons to equal the mass of Earth.

Therefore, the answers to the given questions are: (a) 1027, (b) 106, (c) 102, (d) 1012, (e) 102, (f) 1030.