PHYSICS F/SCIEN.+ENGRS. W/SAPLING >IC<
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ISBN: 9781319336127
Author: Tipler
Publisher: MAC HIGHER
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Chapter 36, Problem 6P
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In a hydrogen atom, the electron is at a distance of 4.768 Å from the nucleus. The angular momentum of the electron is......
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,
L₂ = m₂h,
1 = 0,1,2,..., n-1
m₁ = 0, +1, +2, ..., ±l
3
1
S² = s(s+1)h²=h², S₂ = m₂h = + = h
+/-ħ
4
Consider an excited electron (n > 1) on an H-atom.
What is the minimum angle 0min that the S can have with the z-axis?
Clue: the angle a vector with magnitude V from the z-axis can be computed from
cos 0 = V²/V
The electron of a hydrogen atom is in an orbit with radius of 8.46 Å (1 Å = 10-10 m), according to the Bohr model. Which of the following statements is correct?
a) The total energy of the orbit is –13.6 eV, and the kinetic energy is +13.6 eV.
b) The total energy of the orbit is –0.85 eV, and the potential energy is –1.70 eV.
c) The total energy of the orbit is –0.85 eV, and the potential energy is +1.70 eV.
d) The total energy of the orbit is –0.85 eV, and the potential energy is –0.85 eV.
e) The total energy of the orbit is –3.40 eV, and the potential energy is –6.80 eV.
Chapter 36 Solutions
PHYSICS F/SCIEN.+ENGRS. W/SAPLING >IC<
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- If the angular momentum of an electron atom of hydrogen is equal to 34- ^ 10 × 3.15 j.s, in what orbit is this electron located? And what is his energy.arrow_forwardAngular 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_forwardWhat is the orbital radius of the n = 3 excited state in the Bohr model of the hydrogen atom in nanometers? The ground-state radius of the hydrogen atom is 0.529 × 10-10 m. Please give your answer with 3 decimal places.arrow_forward
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- It may be argued on theoretical grounds that the radius of the hydrogen atom should depend only on the fundamental constants h, e, the electrostatic force constant k = 1/4πℰ0, and m (the electron’s mass). Use dimensional analysis to show that the combination of these factors that yields a result with dimensions of length is h2kme2.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_forwardThe nucleus of a hydrogen atom is a single proton, which has a radius of about 1.1 × 10-15 m. The single electron in a hydrogen atom orbits the nucleus at a distance of 5.3 x 10-¹1 m. What is the ratio of the density of the hydrogen nucleus to the density of the complete hydrogen atom? Number i 1.12E+13 Units (no units)arrow_forward
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