At what radius in Angstroms does the probability of finding an electron at a point in the ground state H atom fall to 70 per cent of its maximum value? (ans. in Angstroms)
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At what radius in Angstroms does the probability of finding an electron at a point in the ground state H atom fall to 70 per cent of its maximum value? (ans. in Angstroms)
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- The quantum-mechanical treatment of the hydrogen atom gives an expression for the wave function ψ, , of the 1s orbital:where ris the distance from the nucleus and a₀ is 52.92 pm. The electron probability density is the probability of finding the elec-tron in a tiny volume at distance rfrom the nucleus and is pro-portional to ψ² . The radial probability distribution is the total probability of finding the electron at all points at distance rfromthe nucleus and is proportional to 4πr² ψ² . Calculate the values(to three significant figures) of ψ, ψ² , and 4πr2² ψ² to fill in the fol-lowing table, and sketch plots of these quantities versus r.In the subshell e = 3, (a) what is the greatest (most positive) me value, (b) how many states are available with the greatest mn, value, and (c) what is the total number of states in the subshell? (a) Number Units (b) Number Units (c) Number UnitsThe total probability of finding an electron in the hydrogen atom is related to the integral ∫ r2 e-2r/ao dr Where r is the distance of the electron from the nucleus and ao is the Bohr radius. Evaluate thisintegral.
- Please asapFor crystal diffraction experiments, wavelengths on the order of 0.25 nm are often appropriate. Find the energy in electron volts for a particle with this wavelength if the particle is (a) a photon; and (b) an electron.The energies in a 2D particle-in-a-box are given by h² 8mL 2 in which the box is a square enclosure with Lx = Ly = L, and nx, ny = 1, 2, 3,... . (a) If the particle is an electron and L = 300 pm (assume three significant figures), find the value of the lowest energy level in units of 10-18 J (that is, if the energy is 5.00 × 10-18 J, you would report it as "5.00"). E n, n (n₂ ² + n₂²) y x y