Please answer the following questions, please include all parts and show steps c

Question

Please answer the following questions, please include all parts and show steps clearly. Thank you for your help.

Calculate the ionization energy of a Be^3+ ion in the state with n = 2. Give you answer in electron volts. Compare this value to the ionization energy of a H atom in the state n = 1. Two spherical harmonic solutions corresponding to l= 1 are Y_1, plusminus 1(theta, phi) = N_1, 1 sin theta e^plusminus i phi. Use these solutions to construct wavefunctions that we associate with p_x and p_y orbitals of the Hydrogen atom. Let the normalization constant be N and the radial part of the function be R. You do not need to evaluate the constant N or the function R. Determine whether the function gamma(theta, phi) = -Y_1, 1(theta, phi) + Y_1, -1(theta, phi) is an eigenfunction of the operator for the z-component of angular momentum l_z. If so, give the eigenvalue.

Explanation / Answer

1) The ionization Energy is givenn by the formula:

E=-13.6*Z2/n2 eV.

For Be3+: Z=4 and n=2

Therefore ,E=-13.6*(4)2/(2)2

=-54.4 eV

Also for Hydrogen in n=1,we have Ionization energy

=-13.6*1/1

=-13.6 eV.

So Ionization Energy of Be3+ is 4*Ionization energy of hydrogen..

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