5. In the Bohr model for hydrogen, the radius of the nth orbit can be shown to be ³ times the radius of the first Bohr orbit r,-0.05 nm (see Example 10.3). Similarly, the energy of an electron in the nth orbit is times its energy when in the n 1 orbit. What is the circumference of the n = 100 orbit? (This is the distance the electron has traveled after having revolved around the proton once.) For such large-n states, the orbital frequency is about equal to the frequency of the photon emitted in a transition from the nth level to an adjacent level with n + 1 or n- 1. Given this, find the frequency and corresponding period of the electron's orbit by computing the frequency associated with the transition from n = 100 to n = 101. Using your values for the electron's orbital size (distance) and travel time (period), calculate the approximate speed of the electron in the 100th orbit. How does this speed compare to the speed of light?

5. In the Bohr model for hydrogen, the radius of the nth orbit can be shown to be ³ times the radius of the first Bohr orbit r,-0.05 nm (see Example 10.3). Similarly, the energy of an electron in the nth orbit is times its energy when in the n 1 orbit. What is the circumference of the n = 100 orbit? (This is the distance the electron has traveled after having revolved around the proton once.) For such large-n states, the orbital frequency is about equal to the frequency of the photon emitted in a transition from the nth level to an adjacent level with n + 1 or n- 1. Given this, find the frequency and corresponding period of the electron's orbit by computing the frequency associated with the transition from n = 100 to n = 101. Using your values for the electron's orbital size (distance) and travel time (period), calculate the approximate speed of the electron in the 100th orbit. How does this speed compare to the speed of light?

Inquiry into Physics

8th Edition

ISBN:9781337515863

Author:Ostdiek

Publisher:Ostdiek

Chapter10: Atomic Physics

Section: Chapter Questions

Problem 8Q

See similar textbooks

Similar questions

How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?
Suppose the velocity of an electron in an atom is known to an accuracy of 2.0103 m/s (reasonably accurate compared with orbital velocities). What is the electron's minimum uncertainty in position, and how does this compare with the approximate 0.1-nm size of the atom?
What is the wavelength of maximum intensity (in nm) and the total energy emitted (in J/s/m2) by a celestial object at 7 K above absolute zero? wavelength of maximum intensity? 414285.71 Total Energy? -----
Compare the gravitational potential energy, mgh, exerted on an electron 100 m above theearths surface to the potential energy exerted on an electron by a hydrogen nucleus at adistance of 1 Angstrom. What does this imply?
Some satellites use nuclear power. (a) If such a satellite emits a 2.35 W flux of ? rays having an average energy of 0.440 MeV, how many are emitted per second? (? rays/s) (b) These ? rays affect other satellites. How far away (in km) must another satellite be to only receive one ? ray per second per square meter?
How do the allowed orbits for electrons in atoms differ from the allowed orbits for planets around the sun? Explain how the correspondence principle applies here.
Observers at a safe distance from atmospheric test of a nuclear bomb feel its heat but receive none of its copious x rays. Why is air opaque to x rays but transparent to infrared?
Check Your Understanding Suppose that two stars, and . radiate exactly the same total power. If the radius of star is three times that of star , what is the ratio of the surface temperatures of these stars? Which one is hotter?
What is a hydrogen-like atom, and how are the energies and radii of its electron orbits related to those in hydrogen?
CT scanners do not detect details smaller than about 0.5 Is this limitation clue to the wavelength of x lays? Explain.
Why does the energy of characteristic x rays become increasingly greater for heavier atoms?
What is the longest wavelength of radiation that can eject a hotoelectron from potassium, given the work function of potassium 2.24 eV? Is it in the visible range?