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.
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.
The light observed that is emitted by a hydrogen atom is explained by a simple model of its structure with one proton in its nucleus and an electron bound to it, but only with internal energies of the atom  satisfying EH=−RH/n2EH=−RH/n2 where RHRH is the Rydberg constant and nn is an integer such as 1, 2, 3 ... and so on.  When a hydrogen atom in an excited state emits light, the photon carries away energy and the atom goes into a lower energy state.  Be careful about units.  The Rydberg constant in eV is  13.605693009 eV   That would be multiplied by the charge on the electron 1.602× 10-19 C to give  2.18× 10-18  J A photon with this energy would have a frequency f such that E=hf.  Its wavelength would be λ = c/f = hc/E.  Sometimes it is handy to measure the Rydberg constant in units of 1/length for this reason.  You may see it given as 109737 cm-1 if you search the web, so be aware that's not joules. The following questions are intended to help you understand the connection between…
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