Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Chapter 39, Problem 16P
(a)
To determine
The proof that the probability of finding the electron in the ground state of hydrogen at less than one Bohr radius from the nucleus is
(b)
To determine
The probability of finding a
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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) Show that the speed of an electron in the nth Bohr orbit of hydrogen is ac/n, where a is
the fine structure constant, equal to e/4neghc. (b) What would be the speed in a hydrogen
like atom with a nuclear charge of Ze?
(a) What is the radius in nm of the electron orbit of a hydrogen atom for n = 4?
(b) What is the energy in eV of the electron above?
Chapter 39 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 39.2 - Prob. 1AECh. 39.2 - Prob. 1BECh. 39.3 - Prob. 1CECh. 39.4 - Prob. 1DECh. 39.4 - Prob. 1EECh. 39.5 - Prob. 1FECh. 39.7 - Prob. 1GECh. 39 - Prob. 1QCh. 39 - Prob. 2QCh. 39 - Prob. 3Q
Ch. 39 - Prob. 4QCh. 39 - Prob. 5QCh. 39 - Prob. 6QCh. 39 - Prob. 7QCh. 39 - Prob. 8QCh. 39 - Prob. 9QCh. 39 - Prob. 10QCh. 39 - Prob. 11QCh. 39 - On what factors does the periodicity of the...Ch. 39 - Prob. 13QCh. 39 - Prob. 14QCh. 39 - Prob. 15QCh. 39 - Prob. 16QCh. 39 - Prob. 17QCh. 39 - Prob. 18QCh. 39 - Prob. 19QCh. 39 - Prob. 20QCh. 39 - Prob. 21QCh. 39 - Prob. 22QCh. 39 - Prob. 23QCh. 39 - Prob. 24QCh. 39 - Prob. 25QCh. 39 - Prob. 26QCh. 39 - Prob. 27QCh. 39 - Prob. 28QCh. 39 - Prob. 29QCh. 39 - Prob. 1PCh. 39 - Prob. 2PCh. 39 - Prob. 3PCh. 39 - Prob. 4PCh. 39 - Prob. 5PCh. 39 - Prob. 6PCh. 39 - Prob. 7PCh. 39 - Prob. 8PCh. 39 - Prob. 9PCh. 39 - Prob. 10PCh. 39 - Prob. 11PCh. 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. 28PCh. 39 - Prob. 29PCh. 39 - Prob. 30PCh. 39 - Prob. 31PCh. 39 - Prob. 32PCh. 39 - Prob. 33PCh. 39 - Prob. 34PCh. 39 - Prob. 35PCh. 39 - Prob. 36PCh. 39 - Prob. 37PCh. 39 - Prob. 38PCh. 39 - Prob. 39PCh. 39 - Prob. 40PCh. 39 - Prob. 41PCh. 39 - Prob. 42PCh. 39 - Prob. 43PCh. 39 - Prob. 44PCh. 39 - Prob. 45PCh. 39 - Prob. 46PCh. 39 - Prob. 47PCh. 39 - Prob. 48PCh. 39 - Prob. 49PCh. 39 - Prob. 50PCh. 39 - Prob. 51PCh. 39 - Prob. 52PCh. 39 - Prob. 53PCh. 39 - Prob. 54PCh. 39 - Prob. 55PCh. 39 - Prob. 56PCh. 39 - Prob. 57PCh. 39 - Prob. 58PCh. 39 - Prob. 59PCh. 39 - Prob. 60PCh. 39 - Prob. 61GPCh. 39 - Prob. 62GPCh. 39 - Prob. 63GPCh. 39 - Prob. 64GPCh. 39 - Prob. 65GPCh. 39 - Prob. 66GPCh. 39 - Prob. 67GPCh. 39 - Prob. 68GPCh. 39 - Prob. 69GPCh. 39 - Prob. 70GPCh. 39 - Prob. 71GPCh. 39 - Prob. 72GPCh. 39 - Prob. 73GPCh. 39 - Prob. 74GPCh. 39 - Prob. 75GPCh. 39 - Prob. 76GPCh. 39 - Prob. 77GP
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- If an atom has an election in the n = 5 state with m = 3, what are the possible values of l?arrow_forwardWhat is the probability that the is electron of a hydrogen atom is found outside the Bohr radius?arrow_forwardWhat is the probability that the Is electron of hydrogen atom is found between r = 0 and r= ?arrow_forward
- Show that the maximum number of electron states the nth shell of an atom is 2n2.arrow_forwardExplain how a hydrogen atom in the ground state (l = 0) can interact magnetically with an external magnetic field.arrow_forwardDo the Balmer series and the Lyman series overlap? Why? Why not? (Hint: calculate the shortest Balmer line and the longest Lyman line.)arrow_forward
- Check Your Understanding Can the magnitude of Lzever be equal to L?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_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
- (6) (a) Show that the speed of an electron in the nth Bohr orbit of hydrogen is ac/n where a is the fine structure constant. (b) What would be the speed in a hydrogenlike atom with a nuclear charge of Ze?arrow_forward(2) In this experiment, why couldn't we observe the series of spectral lines that arise from electrons falling to the ground state, nfinal = 1? This is the Lyman series, for which 22 (see eq. (16)) must be replaced by 12 in both the numerator and denominator of the equation: 2 =- 1 n2 n = R (n2-1)' 2,3,4,5, ..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
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