Modern Physics for Scientists and Engineers
Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Chapter 4, Problem 34P

(a)

To determine

The difference in the various Bohr radii rn  for the hydrogen atom between r1  and r2 .

(b)

To determine

The difference in the various Bohr radii rn  for the hydrogen atom between r5  and r6 .

(c)

To determine

The difference in the various Bohr radii rn  for the hydrogen atom between r10  and r11 .

(d)

To determine

Show that for Rydberg atoms (hydrogen atoms with large n) the difference between successive radii is approximately 2na0 .

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What is the difference in the various Bohr radii rn for the hydrogen atom (a) between r1 and r2, (b) between r5 and r6, and (c) between r10 and r11? (d) Show that for Rydberg atoms the difference between successive radii is approximately 2na0.
A Rydberg hydrogen atom is in the n=45 energy state. (a) What is the energy difference (in eV) between this state and the n=46 level (b) What is the ionization energy of the atom in the n=45 level? (c) What are the frequency and wavelength of a photon emitted in the n=46→n=45 transition? (d ) What is the radius of the atom in the n=45 level? How does this compare with the Bohr radius?
If, in 1 1 = Ry - you set ni = 1 and take n2 greater than 1, you generate what is known as the Lyman %3D series. Find the wavelength of the first mem- ber of this series. The value of ħ is 1.05457 × 10¬34 J.s; the Rydberg constant for hydrogen is 1.09735 × 10’ m¬'; the Bohr radius is 5.29177 × 10¬1" m; and the ground state energy for hydrogen is 13.6057 eV. Answer in units of nm. Consider the next three members of this se- ries. The wavelengths of successive members of the Lyman series approach a common limit as n2 → ∞. What is this limit? Answer in units of nm.
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