a) Calculate, in units of ℏ, the magnitude of the maximum total (orbital+spin) angular momentum for...

a) Calculate, in units of ℏ, the magnitude of the maximum total (orbital+spin) angular momentum for an electron in a hydrogen atom for states with a principal quantum number of 5.

b) An electron initially in a 4p state decays to a lower energy state. Which energy state is forbidden? (pick one): 1s, 2s, 3d, or 2p? Why?

c) What is the total number of electrons that can occupy a subshell for a given amount of orbital angular momentum l? Write an expression in terms of l.

Expert Solution

genius_generous answered 1 year ago

a) Calculate, in units ofℏ, the magnitude of the maximum total (orbital+spin) angular momentum for an...

a) Calculate, in units ofℏ, the magnitude of the maximum total (orbital+spin) angular momentum for an electron in a hydrogen atom for states with a principal quantum number of 5. b) An electron initially in a 4p state decays to a lower energy state. Which energy state is forbidden? (pick one): 1s, 2s, 3d, or 2p? Why? c) What is the total number of electrons that can occupy a subshell for a given amount of orbital angular momentum l? Write...

An electron has spin angular momentum and orbital angular momentum. For the 4 d electron in...

An electron has spin angular momentum and orbital angular momentum. For the 4 d electron in scandium, what percent of its total orbital angular momentum is its spin angular momentum in the z direction?

An electron has spin angular momentum and orbital angular momentum. For the 3.00 d electron in...

An electron has spin angular momentum and orbital angular momentum. For the 3.00 d electron in scandium, what percent of its total orbital angular momentum is its spin angular momentum in the z direction?

Calculate the coupled eigenstates that result from the coupling of orbital angular momentum ?=2 with spin...

Calculate the coupled eigenstates that result from the coupling of orbital angular momentum ?=2 with spin angular momentum ?=1/2. HINT: You may freely use results from Ch. 7 in N. Zettili’s book, including results from the solved problems. Simply quote exactly which result you are using each time.

given an electron has orbital angular momentum and spin angular momentum, l and s respectively. given...

given an electron has orbital angular momentum and spin angular momentum, l and s respectively. given the following relations: [lx,ly] = ih(bar)lz , [ly,lz] = ih(bar)lx , [lz,lx] = ih(bar)ly [sx,sy]= ih(bar) sz , [sy,sz] = ih(bar)sx , [sz, sy\ = ih(bar)sy (a) prove first that for an arbitary operator A, B that AB=BA+[A,B] (b) show that [lx,l^2] = 0 where l^2 = l*l = lx^2 + ly^2 + lz^2 (c) show that similarly, [ly,l^2]=0 and [lz,l^2]=0 (d)given that the...

(a) Calculate the angular momentum of Venus due to its orbital motion about the Sun. In...

(a) Calculate the angular momentum of Venus due to its orbital motion about the Sun. In your calculation, use 1.080 1011 m as the average Venus-Sun distance and 1.940 107s as the period of Venus in its orbit. kg·m2/s (b) Assume that Venus's angular momentum is described by Bohr's assumption . Determine the corresponding quantum number. (c) By what fraction would one have to increase the radius of Venus's circular orbit in order to raise the quantum number by 1?

(a) What is the magnitude of the angular momentum for an ? = 30 electron? ?...

(a) What is the magnitude of the angular momentum for an ? = 30 electron? ? J

1. Calculate the angular momentum of the Sun and compare it to the sum angular momentum...

1. Calculate the angular momentum of the Sun and compare it to the sum angular momentum of the planets (of their orbits only).

A zero-momentum spin stabilized satellite has a momentum wheel spinning at 5000 rpm. The angular momentum...

A zero-momentum spin stabilized satellite has a momentum wheel spinning at 5000 rpm. The angular momentum of the wheel is 100 N-m-sec. a) What is the spin rate of the satellite if its moment of inertia is 500 kg-m2? b) What is the moment of inertial of the wheel? c) If there were a problem with the wheel and it was stopped, what would be the spin rate of the satellite? d) Assuming the problem was fixed, how long would...

The orbital angular momentum is a 3D vector. For an electron at a state associated with...

The orbital angular momentum is a 3D vector. For an electron at a state associated with quantum numbers (?, ?, ??), the magnitude of the orbital angular momentum is √?(? + 1) ℏ. The orbital angular momentum measured along the z axis, however, will be exactly ??ℏ. For a real orbital that combines two complex orbitals associated with two different ?? values, a measurement along the z axis will result in either of the two ?? values with an equal...

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