Show that the wave function ψ100 of the hydrogen atom provides the Schrödinger equation.
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Show that the wave function ψ100 of the hydrogen atom provides the Schrödinger equation.
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- Show that the hydrogen wave function Ψ211 is normalizedCalculate the wavelength of the third line of the Paschen series for hydrogen.Using the concept of standing waves, de Broglie was able to derive Bohr’s stationary orbit postulate. He assumed a confined electron could exist only in states where its de Broglie waves form standing-wave patterns, as in Figure 28.6. Consider a particle confined in a box of length L to be equivalent to a string of length L and fixed at both ends. Apply de Broglie’s concept to show that (a) the linear momentum of this particle is quantized with p=mv = nh/2L and (b) the allowed states correspond to particle energies of En =n2 E0, where E0 = h2/(8mL2).
- The Schrödinger equation is +U(x)\» = E½. 2m dx? Starting from the left, identify each term in the equation.An electron is confined between two perfectly reflecting walls separated by the distance 12 x 10-11m. Use the Heisenberg uncertainty relation to estimate the lowest energy that the particle can have (in eV).Consider the Bohr energy expression (Equation 30.13) as it applies to singly ionized helium He+ (Z = 2) and an ionized atom with Z=5 and only a single electron orbiting the nucleus. This expression predicts equal electron energies for these two species for certain values of the quantum number n (the quantum number is different for each species). For quantum numbers less than or equal to 9, what is the highest energy (in electron volts) for which the helium energy level is equal to the ionized atom energy level?