Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Question
Chapter 39, Problem 36P
To determine
To find:
a) Energy E of hydrogen atom electron
b) Minimum energy needed to remove this electron from the atom
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
(4) Electronic energy level of a hydrogen atom is given by
R
E
; n =
n2
1, 2, 3,...
and R = 13.6 eV. Each energy level has degeneracy 2n² (degeneracy is the number of equivalent
configurations associated with the energy level).
(a) Calculate the partition function Z for a hydrogen atom at a constant temperature.
(b) Let us consider that the energy level of a hydrogen atom is approximated by a two level
system, n = 1,2. Estimate the mean energy at 300 K.
(a) What is the wavelength of light for the least energetic photon emitted in the Balmer series of the hydrogen atom spectrum lines? (b) What is the wavelength of the series limit?
The quantum-mechanical treatment of the hydrogen atom gives an expression for the wave function ψ, , of the 1s orbital:where ris the distance from the nucleus and a₀ is 52.92 pm. The electron probability density is the probability of finding the elec-tron in a tiny volume at distance rfrom the nucleus and is pro-portional to ψ² . The radial probability distribution is the total probability of finding the electron at all points at distance rfromthe nucleus and is proportional to 4πr² ψ² . Calculate the values(to three significant figures) of ψ, ψ² , and 4πr2² ψ² to fill in the fol-lowing table, and sketch plots of these quantities versus r.
Chapter 39 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
Ch. 39 - Prob. 1QCh. 39 - Prob. 2QCh. 39 - Prob. 3QCh. 39 - Prob. 4QCh. 39 - Prob. 5QCh. 39 - Prob. 6QCh. 39 - Prob. 7QCh. 39 - Prob. 8QCh. 39 - Prob. 9QCh. 39 - Prob. 10Q
Ch. 39 - Prob. 11QCh. 39 - Prob. 12QCh. 39 - Prob. 13QCh. 39 - Prob. 14QCh. 39 - Prob. 15QCh. 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. 61PCh. 39 - Prob. 62PCh. 39 - Prob. 63PCh. 39 - Prob. 64PCh. 39 - A diatomic gas molcculc consistsof two atoms of...Ch. 39 - Prob. 66PCh. 39 - Prob. 67PCh. 39 - Prob. 68PCh. 39 - Prob. 69PCh. 39 - Prob. 70PCh. 39 - An old model of a hydrogen atom has the charge e...Ch. 39 - Prob. 72PCh. 39 - Prob. 73P
Knowledge Booster
Similar questions
- (c) Below is the expression of quantized subband energy in a quantum well photodetector where the m* and Wz are the carrier effective mass and well width, respectively, and the rest are constants. Derive the wavelength detected based on intersubband transition. En = ħ2 nn *W. 2m Zarrow_forwardDetermine the integral | P(r) dr for the radial probability density for the ground state of the hydrogen atom 4 P(r) = - r²e-2rla a³ O 1 O-1 O 0.5arrow_forwardAssume that the nucleus of an atom can be regarded as a three-dimensional box of width 2:10-¹4 m. If a proton moves as a particle in this box, find (a) the ground-state energy of proton in MeV and (b) the energies of the first excited state. (c) What are the degenerates of these states? Constants: h = 6.626-10-34 [J-s], m = 1.673-10-27 [kg] and ħ=h/2π.arrow_forward
- (16)arrow_forwardCheck Your Understanding Can the magnitude of Lzever be equal to L?arrow_forward(b) A photon is emitted by a doubly ionised lithium atom (Li²+) when an electron makes a transition to the ground state. The wavelength of the photon is measured to be 10.83 nanometres. Determine the principal quantum number and the energy of the initial state The atomic number of lithium is Z = 3.arrow_forward
- The total probability of finding an electron in the hydrogen atom is related to the integral ∫ r2 e-2r/ao dr Where r is the distance of the electron from the nucleus and ao is the Bohr radius. Evaluate thisintegral.arrow_forwardThe ground-state wave function of a hydrogen atom is: 1 where r is distance from the nucleus and a, is the Bohr radius (53 pm). Following the Born approximation, calculate the probability, i.e., |w?dz, that the electron will be found somewhere within a small sphere of radius, ro, 1.2 pm centred on the nucleus.arrow_forwardAnswer all questions in handwritingarrow_forward
- JC-42) Probability to Find an Electron An electron in its ground state is trapped in the 1D Coulomb potential energy. What is the 0.99ao and x = probability to find it in the region between x = 1.01ao?arrow_forward(b) (deBroglie wave length) Determine the deBroglie wavelength (formula: p=h/2) of a grain of dust with diameter 1um, density 1kg m-3 and speed 1cm s. Compare your result with the diameter of the dust grain and the diameter of an atom. Comment?arrow_forward(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.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax