Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
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Chapter 43, Problem 14SP
To determine
To show: The expression for classical kinetic energy of an electron of the hydrogen atom described by
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(a)
The Lyman series in hydrogen is the transition from energy levels n = 2, 3, 4, ...
to the ground state n =
1. The energy levels are given by
13.60 eV
En
n-
(i)
What is the second longest wavelength in nm of the Lyman series?
(ii)
What is the series limit of the Lyman series?
[1 eV = 1.602 x 1019 J, h = 6.626 × 10-34 J.s, c = 3 × 10° m.s]
%3D
Two emission lines have wavelengts A and + A2, respectively, where AA <<2.
Show that the angular separation A0 in a grating spectrometer is given
aproximately by
(b)
A0 =
V(d/m)-2
where d is the grating constant and m is the order at which the lines are observed.
(a) The L→ K transition of an X-ray tube containing a molybdenum (Z = 42)
target occurs at a wavelength of 0.0724 nm. Use this information to estimate
the screening parameter of the K-shell electrons in molybdenum.
[Osmania University]
A sodium atom (Z = 11) contains 11 protons in its nucleus. Strictly speaking, the Bohr model does not apply, because the neutral atom
contains 11 electrons instead of a single electron. However, we can apply the model to the outermost electron as an approximation,
provided that we use an effective value Zeffective rather than 11 for the number of protons in the nucleus. (a) The ionization energy
for the outermost electron in a sodium atom is 5.1 eV. Use the Bohr model with Z = Zeffective to calculate a value for Zeffective. (b) Using
Z = 11, determine the corresponding value for the radius r of the outermost Bohr orbit. (c) Using the value calculated for Zeffective in
part (a), determine the corresponding radius r of the outermost Bohr orbit.
(a) Zeffective
(b) r =
(c) r=
Number i
Number i
Number i
Units
Units
Units
Chapter 43 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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- A sodium atom (Z = 11) contains 11 protons in its nucleus. Strictly speaking, the Bohr model does not apply, because the neutral atom contains 11 electrons instead of a single electron. However, we can apply the model to the outermost electron as an approximation, provided that we use an effective value Zeffective rather than 11 for the number of protons in the nucleus. (a) The ionization energy for the outermost electron in a sodium atom is 5.1 eV. Use the Bohr model with Z = Zeffective to calculate a value for Zeffective. (b) Using Z = 11, determine the corresponding value for the radius r of the outermost Bohr orbit. (c) Using the value calculated for Zeffective in part (a), determine the corresponding radius r of the outermost Bohr orbit. (a) Zeffective = Number i 2.04 (b) _r= (c)_r= Number i 5.29E-11 Number i 2.12E-11 Units No units Units m Units m ♥arrow_forwardA sodium atom (Z = 11) contains 11 protons in its nucleus. Strictly speaking, the Bohr model does not apply, because the neutral atom contains 11 electrons instead of a single electron. However, we can apply the model to the outermost electron as an approximation, provided that we use an effective value Zeffective rather than 11 for the number of protons in the nucleus. (a) The ionization energy for the outermost electron in a sodium atom is 5.1 eV. Use the Bohr model with Z = Zeffective to calculate a value for Zeffective. (b) Using Z = 11, determine the corresponding value for the radius r of the outermost Bohr orbit. (c) Using the value calculated for Zeffective in part (a), determine the corresponding radius r of the outermost Bohr orbit. (a) Zeffective = Number i (b)_r= (c)_r= Number i Number i Units Units Unitsarrow_forwardThe Lyman series comprises a set of spectral lines. All of these lines involve a hydrogen atom whose electron undergoes a change in energy level, either beginning at the n = 1 level (in the case of an absorption line) or ending there (an emission line). The inverse wavelengths for the Lyman series in hydrogen are given by 1 - where n = 2, 3, 4, ... and the Rydberg constant R, = 1.097 x 10' m-. (Round your answers to at least one decimal place. Enter your answers in nm.) %3D (a) Compute the wavelength for the first line in this series (the line corresponding to n = 2). nm (b) Compute the wavelength for the second line in this series (the line corresponding to n = 3). nm (c) Compute the wavelength for the third line in this series (the line corresponding to n = 4). nm (d) In which part of the electromagnetic spectrum do these three lines reside? O x-ray region O ultraviolet region O infrared region O gamma ray region O visible light regionarrow_forward
- Can nuclei of the same element have different values of Z? Of N? Of A? Can nuclei of different elements have the same values of Z? Of N? Of A?arrow_forwardThe wavelengths of the Lyman series for hydrogen are given by: = RH(1-1), n = 2, 3, 4, ... For the second of this series; calculate the energy (in eV). Note: 1.60 x 10^-19 J = 1.0 eV O 4.10 x 10^3 eV 2.12 x 10^3 eV 3² O 1.21 x 10^3 eV 3.30 x 10^3 eVarrow_forwardForm factor of atomic hydrogen. For the hydrogen atom in its ground state, the number density is n(r) = (7a) exp(-2r/a,), where a, is the Bohr radius. Show that the form factor is fc = 16/(4 + Gʻa)*. %3D %3Darrow_forward
- H-atom. The wave function of one of the electrons in the 2p orbital is given by (ignoring spin) r 2,1,0 (1,0,0)= - 7 exp(-270) c ao 1 |32πα cose Where do is the Bohr radius. In the Bohr model, the radius of the electron orbit is given by m=2 = n²ao = 4ao. The probability that the electron can be found at some radius between r and r + dr is given by 2π P(r) dr = √2 = √ ₁²ª d$ S ² What is the expectation value of the distance of the electron from the nucleus (r)? Clue: expected value is computed by (r) = forP(r) dr then do integration by parts do sin 0 de | Yn.l.m² (r, $,0)|²r² drarrow_forwardConsider the elements selenium (Z = 34), bromine (Z = 35), and krypton (Z = 36). In their part of the periodic table, the subshells of the electronic states are filled in the sequence 1s 2s 2p 3s 3p 3d 4s 4p . . . . What are (a) the highest occupied subshell for selenium and (b) the number of electrons in it, (c) the highest occupied subshell for bromine and (d) the number of electrons in it, and (e) the highest occupied subshell for krypton and (f) the number of electrons in it?arrow_forwardFind the ranges of wavelengths of the Lyman series (=R (-), 2,3,4, ....) and of the Balmer series (=R (-), n = 3,4,5, ....) in the n = emission spectrum of a 1 hydrogen atom. Do these ranges overlap?arrow_forward
- H-atom. The wave function of one of the electrons in the 2p orbital is given by (ignoring spin) 1 r (-2) Cos cos 2,1,0 (r, 0,0) = . 2πT · do |32πα P(r)dr = Where ao is the Bohr radius. In the Bohr model, the radius of the electron orbit is given by ™-2 n²ao = 4ao. The probability that the electron can be found at some radius between r and r + dr is given by r ao TU $ST -exp sin 0 d0 | Yn.l.m² (r, ¢, 0)|²r² dr = What is the most probable distance of the electron from the nucleus? Clue: Most probable r is located at a local maxima of the probability density P(r). Thus, solve for r in a,P(r) = 0arrow_forwardUse the Bohr theory to estimate the wavelength for an n = 3 to n = 1 transition in molybdenum. The measured value is 0.063 nm. Why do we not expect perfect agreement?arrow_forwardFor deuterium (y = 41x106 rad s1 T?), what is the difference in energy between the Wo and 41 states when placed in an 11.7 T magnet?arrow_forward
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