(a) Calculate the most probable value, mp, of finding the electron. (b) Calculate the average value, (r), of finding the electron. (c) Plot both the probability density and the total radial probability density vs. distance in units of Bohr radii for the 1s orbital.
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- What common charateristic do the lines in the Balmer series have? And fundamentally, why would any line in the hydrogen specctrum between 250nm and 700nm belong to the Balmer series?(a) If an electron makes a transition from the n = 6 Bohr orbit to the n = 2 orbit, determine the wavelength of the photon created in the process. 416 nm (b) Assuming that the atom was initially at rest, determine the recoil speed of the hydrogen atom when this photon is emitted.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.
- With the aid of tunable lasers, Rydberg atoms of sodium have been produced with n =100. The resulting atomic diameter would correspond in hydrogen to n = 600.(a) What would be the diameter of a hydrogen atom whose electron is in the n =600 orbit? (b) What would be the speed of the electron in that orbit? (c) How does the result in (b) compare with the speed in the n = 1 orbit?Find (a) the longest wavelength in the Lyman series and (b) theshortest wavelength in the Paschen seriesHow to solve this question