EBK PHYSICS FOR SCIENTISTS & ENGINEERS
5th Edition
ISBN: 9780134296074
Author: GIANCOLI
Publisher: VST
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Question
Chapter 39, Problem 26P
(a)
To determine
The proof that probability of finding the electron within 1 Bohr radius of the nucleus in the hydrogen is
(b)
To determine
The proof that the probability of finding the electron within 1 Bohr radius of the nucleus in the hydrogen is
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Students have asked these similar questions
(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.
(i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in the
actual number with the unit of [eV]. We consider a transition that electron in the 3p state emits
a photon and make a transition to the 2s state. What is the frequency v of this photon ?
(ii) Now we do not include electron spin angular momentum, and just estimate an effect of a
magnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum.
How many lines of optical transition do we expect ? What is the interval of the frequency in the
field B = 0.1 Tesla ?
(iii) In this situation, we do not expect transition from 3s to 2s state if the electron is initially in the
3s state, Explain the reason.
(iv) We now consider an effect of magnetic field B to a free electron spin (not in Hydrogen, but a
free electron). The magnetic field of B = 1.0 Tesla will split the energy level into two (Zeeman)
levels. Obtain the level difference in the unit of [eV] from the value of…
Suppose two electrons in an atom have quantum numbers n = 7 and e = 5. (a) How many states are possible for those two
electrons? (Keep in mind that the electrons are indistinguishable.) (b) If the Pauli exclusion did not apply to the electrons, how
many states would be possible?
Chapter 39 Solutions
EBK PHYSICS FOR SCIENTISTS & ENGINEERS
Ch. 39 - Prob. 2QCh. 39 - Prob. 3QCh. 39 - Prob. 4QCh. 39 - Prob. 5QCh. 39 - Prob. 6QCh. 39 - Prob. 7QCh. 39 - On what factors does the periodicity of the...Ch. 39 - Prob. 9PCh. 39 - Prob. 10PCh. 39 - Prob. 11P
Ch. 39 - Prob. 12PCh. 39 - Prob. 13PCh. 39 - Prob. 14PCh. 39 - Prob. 15PCh. 39 - Prob. 16PCh. 39 - Prob. 17PCh. 39 - Prob. 18PCh. 39 - Prob. 19PCh. 39 - Prob. 20PCh. 39 - Prob. 21PCh. 39 - Prob. 22PCh. 39 - Prob. 23PCh. 39 - Prob. 24PCh. 39 - Prob. 25PCh. 39 - Prob. 26PCh. 39 - Prob. 27PCh. 39 - Prob. 34PCh. 39 - Prob. 35PCh. 39 - Prob. 36PCh. 39 - Prob. 37PCh. 39 - Prob. 40PCh. 39 - Prob. 41PCh. 39 - Prob. 42PCh. 39 - Prob. 43PCh. 39 - Prob. 44PCh. 39 - Prob. 45PCh. 39 - Prob. 46P
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- 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_forwardSuppose two electrons in an atom have quantum numbers n= 2 and L=1 . (a) How many states are possible for those two electrons? (Keep in mind that the electrons are indistinguishable.) (b) If the Pauli exclusion principle did not apply to the electrons, how many states would be possible?arrow_forwardH-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_forward
- The 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(a) Determine the wavelength of the second Balmerline (n=4 to n=2 transition) using Fig. 27–29. Determine likewise (b) the wavelength of the second Lyman line and (c) the wavelength of the third Balmer line.arrow_forwardH-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_forward
- Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is:- 9 3 (1) 31 (2) 27 (3) 23 7 (4) 29arrow_forward(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]arrow_forwardConstruct the energy-level diagram for the He+ ion(like Fig. 27–29).arrow_forward
- (a) Show that the speed of an electron in the nth Bohr orbit of hydrogen is αc/n, where α is the fine structure constant, equal to e2/4πε0ħc. (b) What would be the speed in a hydrogen like atom with a nuclear charge of Ze?arrow_forward(i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in theactual number with the unit of [eV]. We consider a transition that electron in the 3p state emitsa photon and make a transition to the 2s state. What is the frequency ν of this photon ?(ii) Now we do not include electron spin angular momentum, and just estimate an effect of amagnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum.How many lines of optical transition do we expect ? What is the interval of the frequency in thefield B = 0.1 Tesla ?(iii) In this situation, we do not expect transition from 3s to 2s state if the electron is initially in the3s state, Explain the reason.(iv) We now consider an effect of magnetic field B to a free electron spin (not in Hydrogen, but afree electron). The magnetic field of B = 1.0 Tesla will split the energy level into two (Zeeman)levels. Obtain the level difference in the unit of [eV] from the value of magnetic…arrow_forward(i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in theactual number with the unit of [eV]. We consider a transition that electron in the 3p state emitsa photon and make a transition to the 2s state. What is the frequency ν of this photon ?(ii) Now we do not include electron spin angular momentum, and just estimate an effect of amagnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum.How many lines of optical transition do we expect ? What is the interval of the frequency in thefield B = 0.1 Tesla ? Only solve (ii) pleasearrow_forward
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