
Concept explainers
(a)
The differential equation that defines the number of daughter nucleus.
(a)

Answer to Problem 20P
The daughter nucleus satisfies the differential equation is
Explanation of Solution
Let
Write the expression for decay rate
Here,
Write the expression for rate of change of the daughter nuclei
Here,
The rate of decay of the parent nucleus is same as the rate of production of the daughter nuclei.
Substitute
Conclusion:
Substitute
Thus, the daughter nucleus satisfies the differential equation is
(b)
The solution to the above differential equation using the verification by substitution method.
(b)

Answer to Problem 20P
Explanation of Solution
Write the expression for trail solution
Differentiate the above equation with respect to
Multiply equation (V) by
Write the expression for
Conclusion:
Solve (VII) further
Substitute (VIII) in the above equation and rearrange.
Thus,
(c)
The number of
(c)

Answer to Problem 20P
The number of
Explanation of Solution
Write the expression for decay constant
Here,
Substitute
Substitute
Substitute
Substitute
Conclusion:
Using expression (X) and (XI), table the number of
0 | 1000 | 0 |
2 | 445 | 350 |
4 | 408 | 557 |
6 | 261 | 673 |
8 | 167 | 730 |
10 | 107 | 752 |
12 | 68.3 | 751 |
14 | 43.7 | 737 |
16 | 27.9 | 715 |
18 | 17.9 | 689 |
20 | 11.4 | 660 |
22 | 7.30 | 631 |
24 | 4.67 | 602 |
26 | 2.99 | 573 |
28 | 1.91 | 545 |
30 | 1.22 | 519 |
32 | 0.781 | 493 |
34 | 0.499 | 468 |
36 | 0.319 | 445 |
Using the above data in the table construct the graph
Thus, the above graph shows the number of nuclei as a function of time.
(d)
The instant when the number of
(d)

Answer to Problem 20P
The number of
Explanation of Solution
From the above graph, the
(e)
An expression for maximum number of
(e)

Answer to Problem 20P
The time for maximum
Explanation of Solution
Equate (VI) to zero to find the maximum
Conclusion:
Simplify and rearrange for
Here,
Thus, time for maximum
(f)
The instant when the number of
(f)

Answer to Problem 20P
The time when the number of
Explanation of Solution
The time for maximum
Conclusion:
Substitute
Thus, the time when the number of
Want to see more full solutions like this?
Chapter 30 Solutions
Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)
- Two conductors having net charges of +14.0 µC and -14.0 µC have a potential difference of 14.0 V between them. (a) Determine the capacitance of the system. F (b) What is the potential difference between the two conductors if the charges on each are increased to +196.0 µC and -196.0 µC? Varrow_forwardPlease see the attached image and answer the set of questions with proof.arrow_forwardHow, Please type the whole transcript correctly using comma and periods as needed. I have uploaded the picture of a video on YouTube. Thanks,arrow_forward
- A spectra is a graph that has amplitude on the Y-axis and frequency on the X-axis. A harmonic spectra simply draws a vertical line at each frequency that a harmonic would be produced. The height of the line indicates the amplitude at which that harmonic would be produced. If the Fo of a sound is 125 Hz, please sketch a spectra (amplitude on the Y axis, frequency on the X axis) of the harmonic series up to the 4th harmonic. Include actual values on Y and X axis.arrow_forwardSketch a sign wave depicting 3 seconds of wave activity for a 5 Hz tone.arrow_forwardSketch a sine wave depicting 3 seconds of wave activity for a 5 Hz tone.arrow_forward
- The drawing shows two long, straight wires that are suspended from the ceiling. The mass per unit length of each wire is 0.050 kg/m. Each of the four strings suspending the wires has a length of 1.2 m. When the wires carry identical currents in opposite directions, the angle between the strings holding the two wires is 20°. (a) Draw the free-body diagram showing the forces that act on the right wire with respect to the x axis. Account for each of the strings separately. (b) What is the current in each wire? 1.2 m 20° I -20° 1.2 marrow_forwardplease solve thisarrow_forwardplease solve everything in detailarrow_forward
- 6). What is the magnitude of the potential difference across the 20-02 resistor? 10 Ω 11 V - -Imm 20 Ω 10 Ω 5.00 10 Ω a. 3.2 V b. 7.8 V C. 11 V d. 5.0 V e. 8.6 Varrow_forward2). How much energy is stored in the 50-μF capacitor when Va - V₁ = 22V? 25 µF b 25 µF 50 µFarrow_forward9). A series RC circuit has a time constant of 1.0 s. The battery has a voltage of 50 V and the maximum current just after closing the switch is 500 mA. The capacitor is initially uncharged. What is the charge on the capacitor 2.0 s after the switch is closed? R 50 V a. 0.43 C b. 0 66 C c. 0.86 C d. 0.99 C Carrow_forward
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College





