Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 15: Problem 1

If an atom were scaled up to be comparable to the extent of a mid-sized campus, how large would the nucleus be, and what sort of familiar object would be similar?

Short Answer

Expert verified
Answer: When the atom is scaled up to the size of a mid-sized campus, the nucleus would be about 10 centimeters in diameter. A familiar object with a similar size would be a grapefruit or a smaller soccer ball.

Step by step solution

01

Determine the approximate size ratio between the atom and its nucleus

To have an idea about the relative size, we will use the approximate sizes for an atom and its nucleus. Generally, an atom has a diameter of about 10^{-10} meters, or 1 angstrom, while its nucleus has a diameter of about 10^{-14} meters. The ratio between the nucleus and the atom's diameter is therefore: Ratio = (Diameter of nucleus) / (Diameter of atom) = (10^{-14} m) / (10^{-10} m) = 10^{-4} This means that the nucleus is about 10000 times smaller than the atom.
02

Assume a size for a mid-sized campus

Let's assume a mid-sized campus is approximately 1 kilometer (km) or 1000 meters (m) in diameter.
03

Calculate the size of the nucleus in the scaled-up version

Now, using our ratio, we can find the diameter of the nucleus in our scaled-up model. Since we found that the nucleus is about 10000 times smaller than the atom, and our atom is now represented by a diameter of 1000 meters, we can calculate: Diameter of scaled-up nucleus = (Diameter of campus) / 10000 = (1000 m) / 10000 = 0.1 m or 10 centimeters (cm) This means that when the atom is scaled up to the size of a mid-sized campus, the nucleus would be about 10 centimeters in diameter.
04

Find a familiar object with a similar size

Now we need to find a familiar object with a diameter of around 10 cm. A common object that has a diameter close to this size would be a grapefruit or a soccer ball (which has a diameter of around 22 cm). So, in the scaled-up version, the nucleus would be similar in size to a grapefruit or a smaller soccer ball.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A particular fission of \({ }^{235} \mathrm{U}+\mathrm{n}(\) total \(A=236)\) breaks up. One fragment has \(Z=54\) and \(N=86\), making it \({ }^{140} \mathrm{Xe} .\) If no extra neutrons are produced in this event, what must the other fragment be, so all numbers add up? Refer to a periodic table (e.g., Fig. B.1; p. 375 ) to learn which element has the corresponding \(Z\) value, and express the result in the notation \({ }^{\mathrm{A}} \mathrm{X}\).

To illustrate the principle, let's say we start with a nucleus whose mass is \(200.000\) a.m.u. and inject \(1,600 \mathrm{MeV}\) of energy to completely dismantle the nucleus into its constituent parts. How much mass would the final collection of parts have? a) the exact same: \(200.000\) a.m.u. b) less than \(200.000\) a.m.u. c) more than \(200.000\) a.m.u.

The world uses energy at a rate of \(18 \mathrm{TW}\), amounting to almost \(6 \times 10^{20}\) J per year. What is the mass-equivalent \(^{83}\) of this amount of annual energy? What context can you provide for this amount of mass?

Control rods in nuclear reactors tend to contain \({ }^{10} \mathrm{~B}\), which has a high neutron absorption cross section. \(^{81}\) What happens to this nucleus when it absorbs a neutron, and is the result stable? If not, track the decay chain until it lands on a stable nucleus.

Since each nuclear plant delivers \(\sim 1 \mathrm{GW}\) of electrical power, at \(\sim 40 \%\) thermodynamic efficiency this means a thermal generation rate of \(2.5\) GW. How many nuclear plants would we need to supply all 18 TW of our current energy demand? Since a typical lifetime is 50 years before decommissioning, how many days, on average would it be between new plants coming online (while old ones are retired) in a steady state?
See all solutions

Recommended explanations on Environmental Science Textbooks

Environmental Research

Read Explanation

Physical Environment

Read Explanation

Ecology Research

Read Explanation

Living Environment

Read Explanation

Ecological Conservation

Read Explanation

Energy Resources

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free