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 18SP
To determine
The energy pumped into thehydrogen atom to raise it from ground state to the second excited stateby using the figure 43-1.
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(a) How much energy is required to cause an electron in hydrogen to move from the n = 2 state to the n = 5 state?
in J(b) Suppose the atom gains this energy through collisions among hydrogen atoms at a high temperature. At what temperature would the average atomic kinetic energy 3/2 * kBT be great enough to excite the electron? Here kB is Boltzmann's constant.
in K
(a) How much energy is required to cause an electron in hydrogen to move from the n = 2 state to the n = 5 state?in J(b) Suppose the atom gains this energy through collisions among hydrogen atoms at a high temperature. At what temperature would the average atomic kinetic energy 3/2 * kBT be great enough to excite the electron? Here kB is Boltzmann's constant.
in K
v) A hydrogen atom makes a transition from a bound state (Energy of the bound
state = 0.32 eV) to a state with excitation energy (= 10.2 eV). Calculate the
energy of the photon emitted.
Chapter 43 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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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.arrow_forwardThe hydrogen atom was initially at the state where n=3 and l=2. It then decays to a lower state releasing a photon. What are the possible photon energies(in [eV]) that may be observed?arrow_forwardA hydrogen atom initially in its ground state (n=1) absorbs a photon and ends up in the state for which n = 3. What is the energy of the absorbed photon?arrow_forward
- The energy of an electron in a hydrogen atom is -4.45 x 10-20 J. What energy level (n) does it occupy? Is there another valid energy level at -2.69 x 10-20 J? If so, what is this other energy level?arrow_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_forward3. Starting from a thermal energy of phonon in the integral form 3π nD U = - ³7 for ( - II) n² dn hwn [exp(ħwn/t) − 1]) 2 where Debye number n = (6N/π)¹/³, find out the high temperature limit of the thermal energy (= 3NT) and heat capacity (= 3N) of phonon. Iarrow_forward
- Angular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², Lz = m₁h, 1 = 0,1,2,..., n 1 - m₁ = 0, ±1, ±2, ..., ±l 3 S² = s(s+1) h² = =h²₁ 4 Consider an excited electron (n > 1) on an H-atom. The total angular momentum ] = L + Š, whose magnitude and z-component follow a similar dependence to some quantum numbers j and m; as J² = j(j + 1)ħ², Jz = mjħ 1 S₂ = m₂h = ± = h Where j and m; are quantum numbers which assume values that jumps in steps of one such that j is non-negative and −j ≤ m¡ ≤ j. For a given quantum number 1, what are the (two) possible values for j? Clue: we can use the vector sum relation of angular momenta, then consider the z-component only.arrow_forwardAt what radius in the H atom does the radial distribution function of the ground state have (i) 50 per cent, (ii) 75 per cent of its maximum value?arrow_forwardDetermine the energy and frequency of the radiation emitted when an electron falls from n = 4 to n = 2 in a hydrogen atom. [Take m = 9.1×10−31kg, εo=8.85×10−12C2./Nm9.1×10−31kg, ?o=8.85×10−12C2./Nm ]arrow_forward
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