Concept explainers
(a)
The radius of the orbit.
(a)
Answer to Problem 18P
The radius of the orbit is
Explanation of Solution
Write the expression for the radius of any orbit in the hydrogen atom.
Here,
Conclusion:
Substitute
Therefore, the radius of the orbit is
(b)
The linear momentum of the electron.
(b)
Answer to Problem 18P
The linear momentum of the electron is
Explanation of Solution
The condition for the quantization of
Here,
Write the expression for the linear momentum of the electron.
Here,
Use equation (II) in equation (III), to find
Conclusion:
Substitute
Therefore, the linear momentum of the electron is
(c)
The angular momentum of the electron.
(c)
Answer to Problem 18P
The angular momentum of the electron is
Explanation of Solution
Write the expression for the angular momentum of the electron.
Conclusion:
Substitute
Therefore, the angular momentum of the electron is
(d)
The kinetic energy of the electron.
(d)
Answer to Problem 18P
The kinetic energy of the electron is
Explanation of Solution
Write the expression for the kinetic energy of the electron.
Rearrange equation (III) to find the velocity of electron.
Conclusion:
Substitute
Substitute
Therefore, the kinetic energy of the electron is
(e)
The potential energy of the system.
(e)
Answer to Problem 18P
The potential energy of the system is
Explanation of Solution
Write the expression for the potential energy.
Here,
Conclusion:
Substitute
Therefore, the potential energy of the electron is
(f)
The total energy of the system.
(f)
Answer to Problem 18P
The total energy of the system is
Explanation of Solution
Write the expression for the total energy.
Conclusion:
Substitute
Therefore, the total energy of the system is
Want to see more full solutions like this?
Chapter 42 Solutions
Physics for Scientists and Engineers With Modern Physics
- Rank the following quantities of energy from largest to the smallest. State if any are equal. (a) the absolute value of the average potential energy of the SunEarth system (b) the average kinetic energy of the Earth in its orbital motion relative to the Sun (c) the absolute value of the total energy of the SunEarth systemarrow_forwardA space probe is fired as a projectile from the Earths surface with an initial speed of 2.00 104 m/s. What will its speed be when it is very far from the Earth? Ignore atmospheric friction and the rotation of the Earth. P11.26 Ki+Ui=Kf+Uf12mvi2+GMEm(1rf1ri)=12mvf212vi2+GME(01RE)=12vf2orvf2=v122GMEREandvf=(v122GMERE)1/2,vf=[(2.00104)21.25108]1/2m/s=1.66104m/sarrow_forwardA system consists of N identical particles of mass m placed rigidly on the vertices of a regular polygon with each side of length l. If K₁ be the kinetic energy imparted to one of the particles so that it just escapes the gravitational pull of the system and thereafter kinetic energy K₂ is given by to the adjacent particle to escape, then the difference (K₁-K₂) isarrow_forward
- Consider the earth-sun system as a gravitational analog to the hydrogen atom. You may need to know that the mass of the earth is m = 5.97219 × 1024 kg, the mass of the sun is the distance between the sun and the earth is ework 08 M = 1.98847 × 1030 kg, R = 1.49598 × 1011 m, 1 2 and the force and potential energy distribution that the earth experiences due to the gravitational field of the sun are GmM F 7.2 GmM U(r) = - == r where G is the gravitation constant G = 6.67428 × 10-11 N m²/kg². [Some standard calculators have issues with the numbers in this problem. If you get overflow or underflow errors, try using MATLAB] (a) Using the fact that the centripetal force must have magnitude mv2 F = r what is the centripetal velocity of the earth at an arbitrary radius r? (b) Using the centripetal velocity, find the total energy of this system as E=T+U 1 = √mv² + U(r). (c) Use Bohr's assertion that mvr = nh, to find the radii rn as a function of the principle quantum number n for the earth-sun…arrow_forwardConsider the double pendulum shown on figure below. A double pendulum is formed by attaching a pendulum directly to another one. Each pendulum consists of a bob connected to a massless rigid rod which is only allowed to move along a vertical plane. The pivot of the first pendulum is fixed to a point OO. All motion is frictionless. X2 m g 02 marrow_forwardAn asteroid has a mass of m = 2.6 x 106 kg and is approaching Earth. When the asteroid is exactly 3 radii away from the Earth's centre, it's speed relative to the Earth's centre is u = 8.7 x 103 ms-1. The asteroid then falls to the Earth's surface, but remains intact without dissipating any energy as it passes through the Earth's atmosphere. If the rotation of the asteroid and the Earth is ignored, what is the kinetic energy of the asteroid just before it hits the ground? The Earth has mass ME = 5.98 x 1024 kg and a radius of 6.38 x 106 m. To find the relevant potential energies, you must use G = 6.67 x 10-11 N m2 kg-2arrow_forward
- An asteroid has a mass of m = 2.6 x 106 kg and is approaching Earth. When the asteroid is exactly 3 radii away from the Earth's centre, it's speed relative to the Earth's centre is u = 8.7 x 103 ms-1. The asteroid then falls to the Earth's surface, but remains intact without dissipating any energy as it passes through the Earth's atmosphere. If the rotation of the asteroid and the Earth is ignored, what is the kinetic energy of the asteroid just before it hits the ground?arrow_forwardA 1000 kg spacecraft is approaching Jupiter (which is at the origin). The position of the spacecraft is given by the vector RSC = (0.0,-2.533) x 106km. The velocity is given by VSC= (+6.00, +8.00) km/sec. The mass of Jupiter, (MJ=318 MEarth) and MEarth = 5.97 x 1024 kg. A) What is the potential and kinetic energy of the spacecraft (write each to 3 sig figs.) What is the total energy of the spacecraft? Call the total energy Ei. B) Can it escape Jupiter? Justify your answer. C) What is the angular momentum of the spacecraft around Jupiter? Call this Li.arrow_forward13.39 • CALC Consider the ring- shaped object in Fig. E13.39 D. A particle with mass m is placed a distance x from the center of the ring, along the line through the center of the ring and perpendicular to its plane. (a) Calculate the gravitational potential energy U of this system. Take the potential energy to be zero when the two objects are far apart. (b) Show that your answer to part (a) reduces to the expected result when x is much larger than the radius a of the ring. (c) Use F. = -dU/dx to find the magnitude and direction of the force on the particle (see Section 7.4 9). (d) Show that your answer to part (c) reduces to the expected result when x is much larger than a. (e) What are the values of U and F, when x = 0? Explain why these results make sense. Figure E13.39 т Marrow_forward
- The three spheres in the figure, with masses m. = 77 g, ma = 8 g, and m, = 23 g, have their centers on a common line, with L = 21 cm and d = 4 cm. You move sphere B along the line until its center-to-center separation from C is d = 4 cm. How much work is done on sphere B(a) by you and (b) by the net gravitational (a) Number Units (b) Number Unitsarrow_forwardA satellite in Earth orbit has a mass of 96 kg and is at an altitude of 1.98 x 10° m. (Assume that U = 0 as r – ∞.) (a) What is the potential energy of the satellite-Earth system? (b) What is the magnitude of the gravitational force exerted by the Earth on the satellite? 97671.15 What is the equation for gravitational force when the altitude is comparable to the radius of the Earth? N (c) What force, if any, does the satellite exert on the Earth? (Enter the magnitude of the force, if there is no force enter 0.)arrow_forwardThe planet Mars has a mass of 6.39×1023 kilograms (kg) and a radius of 3390 kilometers (km). A satellite is in orbit around Mars, at a height of 2250 km above the surface. The satellite launches a package downwards towards Mars with an initial speed of 1.25 kilometers per second (km/s). How fast will the package be moving when it lands on Mars? Assume that mechanical energy is conserved. Give your answer in units of km/s. 2250 km 1.25 km/sarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning