For a hydrogen atom in the 6f state, what is the minimum angle between the orbital angular momentum vector and the z axis?
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For a hydrogen atom in the 6f state, what is the minimum angle between the orbital
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- The radial probability density of a hydrogen wavefunction in the 1s state is given by P(r) = |4rr2 (R13 (r))²| and the radial wavefunction R1s (r) = a0 , where ao is 3/2 the Bohr radius. Using the standard integral x"e - ka dx n! calculate the standard deviation in the radial position from the nucleus for the 1s state in the Hydrogen atom. Give your answer in units of the Bohr radius ao.Calculate the number of angles that L can make with the z-axis for an l=3 electron.(a) What is the magnitude of the orbital angular momentum in a state with e = 2? (b) What is the magnitude of its largest projection on an imposed axis? (a) Number 2.50998008 Units J.s (b) Number 2.11 Units J.s
- An electron occupying the n = 6 shell of an atom carries z-component orbital angular momentum = (–2) × h/2π. Given that the electron’s total orbital angular momentum is x × h/2π, what is the minimum possible value of number x(remember to use the scientific notation)?If we neglect interaction between electrons, the ground state energy of the helium atom is E =2 z2((- e2)/(2ao)) = -108.848eV (Z=2). The true (measured) value is – 79.006eV.Calculate the interaction energy e2/r12 supposing that both electrons are in the 1s state and r12 that the spin wave function is anti-symmetric. What E is the ground state energy?Suppose you measure the angular momentum in the z-direction L, for an /= 2 hydrogen atom in the state | > 2 > |0 > +i/ |2 >. The eigenvalues of %3D V10 10 Lz are – 2h, -ħ, 0, ħ, 2ħfor the eigenvectors | – 2 >, |– 1>, |0 >, |1 >, |2 >, respectively. What is AL,? V31 10 7 19 25
- (a) How many angles can L make with the z -axis for an l = 2 electron? (b) Calculate the value of the smallest angle.In a particular state of the hydrogen atom, the angle between the angular momentum vector L →and the z-axis is u = 26.6°. If this is the smallest angle for this particular value of the orbital quantum number l, what is l?