Question

Find the order of magnitude of the following physical quantities.

(a) The mass of Earth’s atmosphere: 5.1×10¹8kg.
- a) 10¹6kg
- b) 10¹7kg
- c) 10¹8kg
- d) 10¹9kg

(b) The mass of the Moon’s atmosphere: 25,000 kg.
- a) 10³kg
- b) 10⁴kg
- c) 10⁵kg
- d) 10⁶kg

(c) The mass of Earth’s hydrosphere: 1.4×10²1kg.
- a) 10²0kg
- b) 10²1kg
- c) 10²2kg
- d) 10²3kg

(d) The mass of Earth: 5.97×10²4kg.
- a) 10²3kg
- b) 10²4kg
- c) 10²5kg
- d) 10²6kg

(e) The mass of the Moon: 7.34×10²2kg.
- a) 10²1kg
- b) 10²2kg
- c) 10²3kg
- d) 10²4kg

(f) The Earth–Moon distance (semimajor axis): 3.84×10⁸m.
- a) 10⁶m
- b) 10⁷m
- c) 10⁸m
- d) 10⁹m

(g) The mean Earth–Sun distance: 1.5×10¹1m.
- a) 10⁹m
- b) 10¹0m
- c) 10¹1m
- d) 10¹2m

(h) The equatorial radius of Earth: 6.38×10⁶m.
- a) 10⁵m
- b) 10⁶m
- c) 10⁷m
- d) 10⁸m

(i) The mass of an electron: 9.11×10^−31kg.
- a) 10^−30kg
- b) 10^−31kg
- c) 10^−32kg
- d) 10^−33kg

(j) The mass of a proton: 1.67×10^−27kg.
- a) 10^−25kg
- b) 10^−26kg
- c) 10^−27kg
- d) 10^−28kg

(k) The mass of the Sun: 1.99×10³0kg.
- a) 10²8kg
- b) 10²9kg
- c) 10³0kg
- d) 10³1kg

Answer 1

The order of magnitudes for the given physical quantities are: 10¹8 kg, 10⁴ kg, 10²¹ kg, 10²⁴ kg, 10²² kg, 10⁸ m, 10¹¹ m, 10⁶ m, 10⁻³¹ kg, 10⁻²⁷ kg, 10³⁰ kg.

Step-by-step explanation:

To find the order of magnitude of a physical quantity, we need to determine the power of 10 that best approximates the number. For example, for 5.1 × 10¹8 kg, the order of magnitude is 10¹8 kg, because the power of 10 is 18. Here are the order of magnitudes for the given physical quantities:

1. The mass of Earth's atmosphere: 10¹8 kg
2. The mass of the Moon's atmosphere: 10⁴ kg
3. The mass of Earth's hydrosphere: 10²¹ kg
4. The mass of Earth: 10²⁴ kg
5. The mass of the Moon: 10²² kg
6. The Earth-Moon distance: 10⁸ m
7. The mean Earth-Sun distance: 10¹¹ m
8. The equatorial radius of Earth: 10⁶ m
9. The mass of an electron: 10⁻³¹ kg
10. The mass of a proton: 10⁻²⁷ kg
11. The mass of the Sun: 10³⁰ kg