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Chapter 1: Problem 59

The human body contains about \(10^{14}\) cells, and the diameter of a typical cell is about \(10 \mu \mathrm{m}\). Like all ordinary matter, cells are made of atoms; a typical atomic diameter is \(0.1 \mathrm{nm}\). The mass of a cell is about a. \(10^{-10} \mathrm{kg}\) b. \(10^{-12} \mathrm{kg}\) c. \(10^{-14} \mathrm{kg}\) d. \(10^{-16} \mathrm{kg}\)

Short Answer

Expert verified
The approximate mass of a typical human cell is \(10^{-10}\mathrm{kg}\)

Step by step solution

01

Define the Problem

Identify the meaning of different measurements. The human body contains about \(10^{14}\) cells, the diameter of a typical cell is about \(10 \mu\mathrm{m}\), and a typical atomic diameter is \(0.1\mathrm{nm}\). Now, the problem will be finding an estimated mass of a cell from the choices given.
02

Recognize the Scale

Observe the stark difference in scales between a cell (\(10 \mu \mathrm{m}\)) and an atom (\(0.1\mathrm{nm}\)). As we know that \(\mu \mathrm{m} = 10^{6}\mathrm{nm}\), the diameter of a cell and atom can be written down as \(10*10^{6} \mathrm{nm} = 10^{7}\mathrm{nm}\) for cell and \(0.1\mathrm{nm}\) for Atom. The Cell is approximately 100 million times larger than an atom.
03

Identify the Mass of a Cell

Keeping the scale in mind, if we take the mass of a cell in kilograms (kg), it would be much larger than any atom's mass. For instance, the mass of a hydrogen atom is approximately \(1.67*10^{-27}\) kg. Given this, the mass of a cell should be considerably larger than that. Among the given choices, Option A (\(10^{-10}\) kg) is the largest, and also the closest of the provided options to a reasonable estimation, so it's likely that the mass of a cell is \(10^{-10}\) kg.

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Most popular questions from this chapter

Express the following with appropriate units and significant figures: (a) \(1.0 \mathrm{m}\) plus \(1 \mathrm{mm},\) (b) \(1.0 \mathrm{m}\) times \(1 \mathrm{mm},\) (c) \(1.0 \mathrm{m}\) minus \(999 \mathrm{mm},\) (d) \(1.0 \mathrm{m}\) divided by \(999 \mathrm{mm}\).

Bubble gum's density is about \(1 \mathrm{g} / \mathrm{cm}^{3} .\) You blow an 8 -g wad of gum into a bubble \(10 \mathrm{cm}\) in diameter. What's the bubble's thickness? (Hint: Think about spreading the bubble into a flat sheet. The surface area of a sphere is \(4 \pi r^{2} .\) )

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In nanoseconds, how long is the period of the cesium- 133 radiation used to define the second?

Explain why measurement standards based on laboratory procedures are preferable to those based on specific objects such as the international prototype kilogram.
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