Find the most probable radius for the electron of a hydrogen atom in the 1s and 2p states.
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Find the most probable radius for the electron of a hydrogen atom in the 1s and 2p states.
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- Schematic of the n=3 → n=2 transitions that may occur when a hydrogen atom is placed in a magnetic field B. Ignore the effect of electron spin.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.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 25A hydrogen atom is placed in a 2.4 T magnetic field. What are the possible energy values for a 2p electron with and without magnetic field if we dont consider spin?How many different possible states can there be for an atom with n =5 and l = 1 ?