The spectrum of hydrogen with a nucleus of ﬁnite mass. The analysis in Section I-7 of the text assumes that the nucleus remains ﬁxed as the electronorbits about it. This corresponds to assuming that the proton mass is effectively inﬁnite. More correctly. we should picture the proton and electron as orbiting about their common center of mass. The effects of this can be incorporated in the analysis of Section I-7. but a simpler approach is to use the quantization of angular momentum (Section I-l2) and assume that the permitted circular orbits are those for which the total angular momentum of proton and electron together about the center of mass is nh/2pi (Eq. I-29).
(a) Show that the corrected value of the Rydberg constant Rh is
given by
Rh = [Mp/(Mp + Me)]Rx

where R, is the value for an inﬁnite-mass nucleus.
(bl What is the difference in wavelength for the n = 2 —-> n = 1
"Lyman alpha" transition (A == l2l6 A) calculated using Rx and Rh.respectively?

Solution Summary

The hydrogen with a nucleus of finite mass is examined. Angular momentum quantization are provided.

A H nucleus & a nucleus of yet an unknown atom are stationary at 5.0x10^-10 m apart, Hydrogen atoms mass is mH = 1.7x10^-27kg with an electric charge of e = 1.6x10^-19 C. The Coulomb constant is Ke = 9.0x10^9 Nm^2 C^-2 and that the gravitational constant is G = 6.7x10^-11 N m^2 kg^-2.
Is the force between the hydrogen and the

A simplified model of fusion reaction would have two deuterium atoms (an isotope of hydrogenwith 1 proton and 1 neutron in the nucleus) combine to form an atom of helium. If the mass of each deuterium nucleus is 3.3444 x 10^-27 kg and the mass of the helium nucleus is 6.6465 x 10^-27 kg, how much energy is released when 1 kg o

The mass of the boron nucleus is 11.00657 u. The sum of the masses of the 5 protons and 6 neutrons in this nucleus is 11.08837 u. Calculate the binding energy per nucleus of this boron nucleus. (1 u = 931 MeV)
A) 0.0180 MeV
B) 76.16 MeV
C) 11.381 MeV
D) 7.616 MeV

The "radius of the hydrogen atom" is often taken to be on the order of about 10^-10m. If a measurement is made to determine the location of the electron for hydrogen in its ground state, what is the probability of finding the electron within 10^(-10) m of the nucleus?

The nucleus of the polonium isotope 214Po (mass 214 u) is radioactive and decays by emitting an alpha particle (a helium nucleuswithmass 4 u). Laboratory experiments measure the speed of the alpha particle to be 1.59*10^7 m/s . Assuming the polonium nucleus was initially at rest, what is the recoil velocity of the nucleus that

A proton, which is the nucleus of a hydrogen atom, can be modeled as a sphere with a diameter of 2.4 fm and a mass of 1.67 10^(-27) kg. Determine the density of the proton in kg/m^3 and show all work.

A singly ionized helium atom (He+) has only one electron in orbit about the nucleus. What is the radius of the ion when it is in the n = 3 excited state?
I have an idea of how to do the problem, but that is withhydrogen. Please help and thank you very much!

Muonir atoms and the size of the nucleus. The negative muon (symbol pf) is a particle with the same charge as the electron but with a larger mass (m = 207 m,). High-speed muons are produced in violent nuclear collisions. These muons can be slowed down in matter and captured into orbits around the nuclei of atoms in the material.