(a)
The probability of finding the electron in the region between
(a)
Answer to Problem 41P
The probability of finding the electron in the region between
Explanation of Solution
Given:
The value of
The value of
The value of
The value of
The value of
Formula used:
The expression for probabilityis given by,
The expression for
The expression for
The expression for
Calculation:
The probability is calculated as,
Solving further as,
For
Conclusion:
Therefore, the probability of finding the electron in the region between
(b)
The probability of finding the electron in the region between
(b)
Answer to Problem 41P
The probability of finding the electron in the region between
Explanation of Solution
Given:
The value of
The value of
The value of
The value of
The value of
Formula used:
The expression for probability is given by,
The expression for
The expression for
The expression for
Calculation:
The probability is calculated as,
Solving further as,
For
Conclusion:
Therefore, the probability of finding the electron in the region between
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Chapter 36 Solutions
Physics for Scientists and Engineers
- Consider a two-electron spin system in a singlet state. a. If a measurement of one of the electrons shows that it is in a state with sz = 1/2, what is the probability of obtaining another state with sz= +1/2? b. If a measurement of one of the electrons shows that it is in a state with sx = 1/2, what is the probability of obtaining another state with sy = +1/2?arrow_forwardConsider hydrogen in the ground state, 100 . (a) Use the derivative to determine the radial position for which the probability density, P(r), is a maximum. (b) Use the integral concept to determine the average radial position. (This is called the expectation value of the electrons radial position.) Express your answers into terms of the Bohr radius, a0. Hint: The expectation value is the just average value, (c) Why are these values different?arrow_forwardConsider two non-identical particles, each with spin 1/2. One particle is in a state with Siy = h/2. The other is in a state with Szx = - ħ/2. What is the probability of finding the system in a state with total spin s = 0? %3D %3Darrow_forward
- ▼ Part A For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 1.00×10-2 ap at distance aB? ▸ View Available Hint(s) 15. ΑΣΦ ? Part B For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 1.00×10-2 ag at distance ag from the proton? ▸ View Available Hint(s) [5] ΑΣΦ ? Submit Submitarrow_forwardIn a one-dimensional system, the density of states is given by N(E)= 2m, where L is the length of the sample L√2m in the and m is the mass of the electron, as seen in class. There are N quantum particles with spin |S| = sample (the quantum particles can be understood as 'special electrons with spin [S] ='), so that each state can be occupied by 2|S| + 1 particles. Determine the Fermi energy at 0 K.arrow_forwardAnswer the following. (a) Write out the electronic configuration of the ground state for nitrogen (Z = 7). 1s22s22p11s22s22p2 1s22s22p31s22s22p41s22s22p51s22s22p6 (b) Write out the values for the set of quantum numbers n, ℓ, m, and ms for each of the electrons in nitrogen. (In cases where there are more than one value, enter the positive value first. Enter positive values without a '+' sign in front of them. Include all possible values.) 1s states n = ℓ = m = ms = ms = 2s states n = ℓ = m = ms = ms = 2p states n = ℓ = m = ms = ms = m = ms = ms = m = ms = ms =arrow_forward
- A potential well has 4 energy levels as given here: Energy of the state (eV) 13 12 9 4 Suppose that there are three electrons in the well, and that the system is in the first excited state. If the system emits a photon, what energy could the photon have? O (a) 3 eV Ⓒ (b) 5 eV O (c) 4 eV O (d) 8 eV (e) 9 eV x X 0%arrow_forwardHow many electrons can occupy the system with l=0, l=2 and l=4. What is number of possible orientations of the orbital angular momentum with l=4? What is the smallest z-component of the orbital angular momentum?arrow_forwardAssume that electrons in a 2- dimensional system has a linear dispersion relation: E = ~vFk, where vF is theFermi velocity. Obtain the density of states (DOS) for these electrons.arrow_forward
- Suppose a system contain four identical particles and five energy levels given by the relationship, E;= i × 10-2º J, where i = 0,1,2 ,3,4. If the total energy of the system is Er= 6 E. Find the total number of the microscopic states for the distribution of these particles over the system energy levels keeping the given system conditions. Solution 4 identical particles Energy (10- Joule) Macroscopic state 4 Er= 6 € 3 Levels 1 E2 E (10-º J) k 1 2 4 5 6 7 N! Wk no! n!n2!n3!n4! Sk = kglnwkarrow_forwardA thin solid barrier in the xy-plane has a 12.6µm diameter circular hole. An electron traveling in the z-direction with vx 0.00m/s passes through the hole. Afterward, within what range is vx likely to be?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, 1 = 0,1,2,..., n-1 Lz = m₂ħ, m₁ = 0, ±1, ±2,..., ±l 3 S² = s(s+1)h² = h², 4 Consider an excited electron (n > 1) on an H-atom. Sz = msh 1 =+=ħ Show that the minimum angle that the I can have with the z-axis is given by n-1 n L.min = cos Clue: the angle a vector with magnitude V from the z-axis can be computed from cos 0 = V²/Varrow_forward
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