bartleby

Concept explainers

Question
Book Icon
Chapter 30, Problem 43P

(a)

To determine

The radius of the 612C nucleus.

(a)

Expert Solution
Check Mark

Answer to Problem 43P

The radius of the 612C nucleus is 2.7fm_.

Explanation of Solution

Write the expression for the radius of the 612C nucleus.

    r=aA1/3        (I)

Here, r is the radius of the 612C nucleus, A is the mass number, a is a constant.

Conclusion:

Substitute 1.2fm for a, 12 for A in equation (I) to find r.

    r=(1.2fm×1015m1fm)(12)1/3=2.7×1015m=2.7fm

Therefore, the radius of the 612C nucleus is 2.7fm_.

(b)

To determine

The force of repulsion between a proton at the surface of an 612C nucleus and the remaining five protons.

(b)

Expert Solution
Check Mark

Answer to Problem 43P

The force of repulsion between a proton at the surface of an 612C nucleus and the remaining five protons 1.5×102N_.

Explanation of Solution

Write the expression for the force of repulsion between a proton at the surface of an 612C nucleus and the remaining five protons.

    F=ke(Z1)e(1e)r2=ke(Z1)e2r2        (II)

Here, F is the force of repulsion between a proton at the surface of an 612C nucleus and the remaining five protons, ke is the columbic constant, r is the radius of the nucleus, Z is the number of protons, e is the electronic charge.

Conclusion:

Substitute 8.99×109Nm2/C2 for ke, 6 for Z, 2.7fm for r, 1.60×1019C for e in equation (II) to find F.

    F=(8.99×109Nm2/C2)(61)(1.60×1019C)2(2.7fm×1015m1fm)2=1.5×102N

Therefore, the force of repulsion between a proton at the surface of an 612C nucleus and the remaining five protons 1.5×102N_.

(c)

To determine

The work done to overcome the last proton from a large distance up to the surface of the nucleus.

(c)

Expert Solution
Check Mark

Answer to Problem 43P

The work done to overcome the last proton from a large distance up to the surface of the nucleus is 2.6MeV_.

Explanation of Solution

Write the expression for the work done to overcome the last proton from a large distance up to the surface of the nucleus.

    U=ke(Z1)e(1e)r=ke(Z1)e2r        (III)

Conclusion:

Substitute 8.99×109Nm2/C2 for ke, 6 for Z, 2.7fm for r, 1.60×1019C for e in equation (II) to find U.

    U=(8.99×109Nm2/C2)(61)(1.60×1019C)2(2.7fm×1015m1fm)=4.2×1013JU(in MeV)=(4.2×1013J×1MeV1.60×1013J)=2.6MeV

Therefore, the work done to overcome the last proton from a large distance up to the surface of the nucleus is 2.6MeV_.

(d)

To determine

The radius of 92238U nucleus, the force between a proton at the surface of 92238U and the remaining protons, the work done to overcome the last proton from a large distance up to the surface of the nucleus.

(d)

Expert Solution
Check Mark

Answer to Problem 43P

The radius of 92238U nucleus is 7.4fm_, the force between a proton at the surface of 92238U and the remaining protons is 3.8×102N_, the work done to overcome the last proton from a large distance up to the surface of the nucleus is 18MeV_.

Explanation of Solution

Use equation (I) to solve for the radius of 92238U nucleus.

Use equation (II) to solve for force between a proton at the surface of 92238U and the remaining protons.

Use equation (III) the work done to overcome the last proton from a large distance up to the surface of the nucleus.

Conclusion:

Substitute 1.2fm for a, 238 for A in equation (I) to find r.

    r=(1.2fm×1015m1fm)(238)1/3=7.4×1015m=7.4fm

Substitute 8.99×109Nm2/C2 for ke, 92 for Z, 7.4fm for r, 1.60×1019C for e in equation (II) to find F.

    F=(8.99×109Nm2/C2)(921)(1.60×1019C)2(7.4fm×1015m1fm)2=3.8×102N

Substitute 8.99×109Nm2/C2 for ke, 92 for Z, 7.4fm for r, 1.60×1019C for e in equation (II) to find U.

    U=(8.99×109Nm2/C2)(921)(1.60×1019C)2(7.4fm×1015m1fm)=2.8×1012JU(in MeV)=(2.8×1012J×1MeV1.60×1013J)=18MeV

Therefore, the radius of 92238U nucleus is 7.4fm_, the force between a proton at the surface of an 92238U and the remaining protons is 3.8×102N_, the work done to overcome the last proton from a large distance up to the surface of the nucleus is 18MeV_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Four capacitors are connected as shown in the figure below. (Let C = 12.0 μF.) a C 3.00 με Hh. 6.00 με 20.0 με HE (a) Find the equivalent capacitance between points a and b. 5.92 HF (b) Calculate the charge on each capacitor, taking AV ab = 16.0 V. 20.0 uF capacitor 94.7 6.00 uF capacitor 67.6 32.14 3.00 µF capacitor capacitor C ☑ με με The 3 µF and 12.0 uF capacitors are in series and that combination is in parallel with the 6 μF capacitor. What quantity is the same for capacitors in parallel? μC 32.14 ☑ You are correct that the charge on this capacitor will be the same as the charge on the 3 μF capacitor. μC
In the pivot assignment, we observed waves moving on a string stretched by hanging weights. We noticed that certain frequencies produced standing waves. One such situation is shown below: 0 ст Direct Measurement ©2015 Peter Bohacek I. 20 0 cm 10 20 30 40 50 60 70 80 90 100 Which Harmonic is this? Do NOT include units! What is the wavelength of this wave in cm with only no decimal places? If the speed of this wave is 2500 cm/s, what is the frequency of this harmonic (in Hz, with NO decimal places)?
Four capacitors are connected as shown in the figure below. (Let C = 12.0 µF.) A circuit consists of four capacitors. It begins at point a before the wire splits in two directions. On the upper split, there is a capacitor C followed by a 3.00 µF capacitor. On the lower split, there is a 6.00 µF capacitor. The two splits reconnect and are followed by a 20.0 µF capacitor, which is then followed by point b. (a) Find the equivalent capacitance between points a and b. µF(b) Calculate the charge on each capacitor, taking ΔVab = 16.0 V. 20.0 µF capacitor  µC 6.00 µF capacitor  µC 3.00 µF capacitor  µC capacitor C  µC

Chapter 30 Solutions

Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, Multi-Term

Ch. 30 - Prob. 5OQCh. 30 - Prob. 6OQCh. 30 - Prob. 7OQCh. 30 - Prob. 8OQCh. 30 - Prob. 9OQCh. 30 - Prob. 10OQCh. 30 - Which of the following quantities represents the...Ch. 30 - Prob. 12OQCh. 30 - Prob. 1CQCh. 30 - Prob. 2CQCh. 30 - Prob. 3CQCh. 30 - Prob. 4CQCh. 30 - Prob. 5CQCh. 30 - Prob. 6CQCh. 30 - Prob. 7CQCh. 30 - If no more people were to be born, the law of...Ch. 30 - Prob. 9CQCh. 30 - Prob. 10CQCh. 30 - Prob. 11CQCh. 30 - What fraction of a radioactive sample has decayed...Ch. 30 - Prob. 13CQCh. 30 - Prob. 14CQCh. 30 - Prob. 15CQCh. 30 - Prob. 16CQCh. 30 - Prob. 17CQCh. 30 - Prob. 1PCh. 30 - Prob. 2PCh. 30 - Prob. 3PCh. 30 - Prob. 4PCh. 30 - Prob. 5PCh. 30 - Prob. 6PCh. 30 - Prob. 7PCh. 30 - Prob. 8PCh. 30 - Prob. 9PCh. 30 - Prob. 10PCh. 30 - Prob. 11PCh. 30 - Prob. 12PCh. 30 - Prob. 13PCh. 30 - Prob. 14PCh. 30 - Prob. 16PCh. 30 - Prob. 17PCh. 30 - Prob. 18PCh. 30 - What time interval elapses while 90.0% of the...Ch. 30 - Prob. 20PCh. 30 - Prob. 21PCh. 30 - Prob. 22PCh. 30 - Prob. 23PCh. 30 - Prob. 24PCh. 30 - Prob. 25PCh. 30 - Prob. 26PCh. 30 - Prob. 27PCh. 30 - Prob. 28PCh. 30 - Prob. 29PCh. 30 - Prob. 30PCh. 30 - Prob. 31PCh. 30 - Prob. 32PCh. 30 - Prob. 33PCh. 30 - Prob. 34PCh. 30 - Prob. 35PCh. 30 - Prob. 36PCh. 30 - Prob. 37PCh. 30 - Prob. 38PCh. 30 - Prob. 39PCh. 30 - Prob. 41PCh. 30 - Prob. 42PCh. 30 - Prob. 43PCh. 30 - Prob. 45PCh. 30 - Prob. 46PCh. 30 - Prob. 47PCh. 30 - Prob. 48PCh. 30 - Prob. 49PCh. 30 - Prob. 50PCh. 30 - Prob. 51PCh. 30 - Prob. 52PCh. 30 - Prob. 53PCh. 30 - Prob. 54PCh. 30 - Prob. 55PCh. 30 - Prob. 56PCh. 30 - Prob. 57PCh. 30 - Prob. 58PCh. 30 - Prob. 59PCh. 30 - Prob. 60PCh. 30 - Prob. 61PCh. 30 - Prob. 62PCh. 30 - Prob. 63PCh. 30 - Prob. 64PCh. 30 - Prob. 65PCh. 30 - Prob. 66PCh. 30 - Prob. 67PCh. 30 - Prob. 68PCh. 30 - Prob. 69PCh. 30 - Prob. 70P
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
Text book image
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Text book image
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning