Quantum Mechanical Model Of Atom

Energy of electron in nth orbit of hydrogen atom is : Now for shortest wavelength in Lyman series, the transition of atom takes place from infinity to n = 1 i.e., Again for longest wavelength in Lyman series, the transition of electron is from

To solve this problem, we need to use Heisenberg's uncertainty principle, which is given by the relation: where: - is the uncertainty in position, - is the uncertainty in momentum, - is the reduced Planck's constant, . The uncertainty in momentum can be written as: where: - (mass of the proton), - . The velocity of the proton is given as , where . Therefore: Now, the uncertainty in velocity is: Now, calculate the uncertainty in momentum : Using the uncertainty principle: Substitute the known values: Therefore, the uncertainty in the position is .

The electronic configuration of Lutetium (Lu) is: For the tripositive state (Lu ), 3 electrons are removed, which will affect the and orbitals. The valence electrons left are in the subshell, and the 4f orbital corresponds to and . Thus, the correct quantum numbers are and .