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Chapter 5: Q20E (page 187)

A comet in an extremely elliptical orbit about a star has, of course, a maximum orbit radius. By comparison, its minimum orbit radius may be nearly 0. Make plots of the potential energy and a plausible total energyversus radius on the same set of axes. Identify the classical turning points on your plot.

Short Answer

Expert verified

The graph is given as,

Step by step solution

01

Given data

A comet has an extremely elliptical orbit about a star. The minimum value of the orbit radius is nearly zero as compared to the maximum orbit radius.

Write the expression for the potential energy of the comet.

Uc=-GMmr

Here, Uc is the potential energy of the comet, G is the gravitational constant, M is the mass of the star, m is the mass of the comet and r is the distance of the comet from the star.

02

Concept of potential energy

The potential energy of the comet varies inversely with its position.

03

Step 3:

The potential energy of the comet varies inversely with its position.

The diagram given below shows the variation of the potential energy and the total energy of the comet.

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Most popular questions from this chapter

Summarize the similarities are differences between the three simple bound cases considered in this chapter.

The quantized energy levels in the infinite well get further apart as n increases, but in the harmonic oscillator they are equally spaced.

  1. Explain the difference by considering the distance 鈥渂etween the walls鈥� in each case and how it depends on the particles energy
  2. A very important bound system, the hydrogen atom, has energy levels that actually get closer together as n increases. How do you think the separation between the potential energy 鈥渨alls鈥� in this system varies relative to the other two? Explain.

What is the probability that the particle would be found between x = 0and x = 1/a?

Consider a particle of mass mand energy E in a region where the potential energy is constant U0. Greater than E and the region extends tox=+鈭�

(a) Guess a physically acceptable solution of the Schrodinger equation in this region and demonstrate that it is solution,

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(c) The particle鈥檚 mass m is 10-3 kg. By how much (in eV) doesthe potential energy prevailing from x=1 nm to U0. Exceed the particle鈥檚 energy?

A 2kg block oscillates with an amplitude of 10cm on a spring of force constant 120 N/m .

(a) In which quantum state is the block?

(b) The block has a slight electric charge and drops to a lower energy level by generating a photon. What is the minimum energy decrease possible, and what would be the corresponding fractional change in energy?
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