Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 29, Problem 6OQ
To determine
Select the correct option for a hydrogen atom with its electron in the
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An electron is in a hydrogen atom with n = 2 and ℓ = 1.
(a) Find all the possible angles between the orbital angular momentum vector and the z-axis.
(b) Suppose the atom absorbs a photon and rises from the n = 2 and ℓ = 1 state to the n = 3 state. Using conversation of angular momentum, what are the possible values of the final value of ℓ in the n = 3 state?
Which of the following is a permissable set of quantum numbers for an electron in a hydrogen atom? The atom may be in an excited state (ie. the electron need not be in its ground state).
a) n = 6, l = -5, ml = +4, ms = +1/2
b) n = 4, l = -2, ml = +2, ms = -1/2
c) n = 2, l = 2, ml = +1, ms = -1/2
d) n = 5, l = 1, ml = -1, ms = +1/2
e) n = 3, l = 2, ml = -2, ms = -1
A hydrogen atom is in its first excited state (n = 2). Using the Bohr theory of the atom, calculate the following.
(a) the radius of the orbit
nm
(b) the linear momentum of the electron
kg. m/s
(c) the angular momentum of the electron
J.s
(d) the kinetic energy
eV
(e) the potential energy
eV
Chapter 29 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 29.2 - Prob. 29.1QQCh. 29.2 - Prob. 29.2QQCh. 29.4 - Prob. 29.3QQCh. 29.5 - Prob. 29.4QQCh. 29.6 - Prob. 29.5QQCh. 29.6 - Prob. 29.6QQCh. 29 - Prob. 1OQCh. 29 - Prob. 2OQCh. 29 - Prob. 3OQCh. 29 - Prob. 4OQ
Ch. 29 - Prob. 5OQCh. 29 - Prob. 6OQCh. 29 - Prob. 7OQCh. 29 - Prob. 8OQCh. 29 - Prob. 9OQCh. 29 - Prob. 10OQCh. 29 - Prob. 1CQCh. 29 - Prob. 2CQCh. 29 - Prob. 3CQCh. 29 - Prob. 4CQCh. 29 - Prob. 5CQCh. 29 - Prob. 6CQCh. 29 - Prob. 7CQCh. 29 - Prob. 8CQCh. 29 - Prob. 9CQCh. 29 - Prob. 10CQCh. 29 - Prob. 1PCh. 29 - Prob. 2PCh. 29 - Prob. 3PCh. 29 - Prob. 4PCh. 29 - Prob. 5PCh. 29 - Prob. 6PCh. 29 - Prob. 7PCh. 29 - Prob. 8PCh. 29 - Prob. 10PCh. 29 - Prob. 11PCh. 29 - Prob. 12PCh. 29 - Prob. 13PCh. 29 - Prob. 14PCh. 29 - Prob. 15PCh. 29 - Prob. 16PCh. 29 - Prob. 17PCh. 29 - Prob. 18PCh. 29 - Prob. 19PCh. 29 - Prob. 20PCh. 29 - Prob. 21PCh. 29 - Prob. 22PCh. 29 - Prob. 23PCh. 29 - Prob. 24PCh. 29 - Prob. 25PCh. 29 - Prob. 26PCh. 29 - Prob. 27PCh. 29 - Prob. 28PCh. 29 - Prob. 29PCh. 29 - Prob. 30PCh. 29 - Prob. 31PCh. 29 - Prob. 32PCh. 29 - Prob. 33PCh. 29 - Prob. 34PCh. 29 - Prob. 35PCh. 29 - Prob. 36PCh. 29 - Prob. 37PCh. 29 - Prob. 38PCh. 29 - Prob. 39PCh. 29 - Prob. 40PCh. 29 - Prob. 41PCh. 29 - Prob. 42PCh. 29 - Prob. 43PCh. 29 - Prob. 44PCh. 29 - Prob. 45PCh. 29 - Prob. 46PCh. 29 - Prob. 47PCh. 29 - Prob. 48PCh. 29 - Prob. 49PCh. 29 - Prob. 50PCh. 29 - Prob. 51PCh. 29 - Prob. 52PCh. 29 - Prob. 53PCh. 29 - Prob. 54PCh. 29 - Prob. 55PCh. 29 - Prob. 57PCh. 29 - Prob. 58PCh. 29 - Prob. 59PCh. 29 - Prob. 60PCh. 29 - Prob. 61PCh. 29 - Prob. 63PCh. 29 - Prob. 64PCh. 29 - Prob. 65PCh. 29 - Prob. 66P
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- For an electron in a hydrogen atom in the n=2 state, compute: (a) the angular momentum; (b) the kinetic energy; (c) the potential energy; and (d) the total energy.arrow_forwardFor a hydrogen atom in an excited state with principal quantum number n, show that the smallest angle that the orbital angular momentum vector can make with respect to the z-axis is =cos1( n1n) .arrow_forwardWhich of the following sets of quantum numbers can be used to describe the 2 electrons in the He atom? For the possible sets, write the electron configuration and identify if it is a ground state or excited state configuration. i) n = 2,1 = 0, mį = 0, mş = 1/2 and n = 1, 1 = 0, m = 0, mş = 1/2 ii) n = 2,1= 0, mi = 0, ms = 1/2 and n = 2,1= 0, mi = 0, ms = 1/2 iii) n = 2,1= 1, mị = 0, mş = 1/2 and n = 2,1= 0, mį = 0, ms = 1/2 iv) n = 2,1= 0, mį = 0, ms =- 1/2 and n = 2,1= 0, m¡ = 0, ms = 1/2 v) n = 1,1= 0, mį = 0, mş = 2 and n = 1,1 = 0, mį = 0, mş = -2 %3D %3D %3D %3Darrow_forward
- a) Use the Bohr model of the atom to calculate the orbiting speed of the electron in the n = 5 state. b) What is the principal quantum number n for which the orbiting period of the electron is about one picosecond? (1 ps = 1 × 10^−12 s)arrow_forwardA hydrogen atom is in its third excited state (n = 4). Using the Bohr theory of the atom, calculate the following. (a) the radius of the orbit nm (b) the linear momentum of the electron kg • m/s (c) the angular momentum of the electron J.S (d) the kinetic energy eV (e) the potential energy eV (f) the total energy eVarrow_forwarda) Use the Bohr model of the atom to calculate the orbiting speed of the electron in the n = 5 state. What is the principal quantum number n for which the orbiting period of the electron is about one picosecond? (1 ps = 1 × 10−12 s)arrow_forward
- A hydrogen atom is in the 6g state. (a) What is the principal quantum number? (b) What is the energy of the atom? (c) What are the values for the orbital quantum number and the magnitude of the electron’s orbital angular momentum? (d) What are the possible values for the magnetic quantum number? For each value, find the corresponding z component of the electron’s orbital angular momentum and the angle that the orbital angular momentum vector makes with the z-axis.arrow_forwardA hydrogen atom is in its second excited state (n = 3). Using the Bohr theory of the atom, calculate the following. (a) the radius of the orbit nm(b) the linear momentum of the electron kg · m/s(c) the angular momentum of the electron J · s(d) the kinetic energy eV(e) the potential energy eV(f) the total energy eVarrow_forwardAn electron is in the n = 4, l = 3 state of the hydrogen atom. (a) What is the length of the electron's angular momentum vector? (b) How many different possible z components can the angular momentum have? List the possible z components. (c) What are the values of the angle that the angular momentum vector, L, makes with the z-axis? (d) Would your answers to (a), (b) or (c) change if the principal quantum number were n = 5 instead of n = 4?arrow_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_forwardLight of wavelength 102.6 nm is emitted by a hydrogen atom. What are the (a) higher quantum number and (b) lower quantum number of the transition producing this emission? (c) What is the name of the series that includes the transition?arrow_forward
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