Find the three-dimensional Fourier transform of the wave function of a 1s electron in the hydrogen atom (where a0 is the radius of the orbit): ψ1s(r) = (1/((πa02 )^1/2))exp(-r/a0)
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Find the three-dimensional Fourier transform of the wave function of a 1s electron in the hydrogen atom (where a0 is the radius of the orbit):
ψ1s(r) = (1/((πa02 )^1/2))exp(-r/a0)
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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.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 the Normalization constant A of the Hydrogen atom wave function at t = 0 |Ψ(0)> = A(3i*|100> - 4*|211> + |210> + sqrt(10)*|21-1>) Where |100>, |210> |211>, and |21-1> represent Ψnlm respectively
- X-ray is produced by bombarding a tungsten target with high energy electrons accelerated by 8.8 kV of voltage. Use σ = 1 for the electron transition down to K shell (n = 1) and σ = 7.4 for the electron transition down to L shell (n = 2) for characteristic X-ray. What is energy of the characteristic X-ray of the tungsten (Z = 74) target when the electron in n = 4 orbital moves down to n = 1? What is the energy the characteristic X-ray of the tungsten (Z = 74) target when the electron in n = 3 orbital moves down to n = 2?H-alpha line is a red visible spectral line in hydrogen atom with a wavelength of 656.3 nm. Consider five distant stars labeled A, B, C, D, and E. The light from these starts was detected on Earth and, after performing spectral analysis, the following H-alpha wavelengths were measured: AA = 667.5 nm, Ag = 650.4 nm, Ac = 653.5 nm, Ap = 660.3 nm, and AE = 664.9 nm. Which star has the slowest speed relative to Earth, in which direction and how fast does it move? The slowest star is? and it moves Select an answer The speed of the slowest star (in km/s), Vslowest = Which star has the fastest speed relative to Earth, in which direction and how fast does it move? The fastest star is? and it moves Select an answer Earth. The speed of the fastest star (in km/s), Vfastest Submit Question = Earth. Units Select an answer ✓ Units Select an answer ✓5 6 À (x10-² nm) 7 8 9 10 Relative intensity Mo 9 9 12 vith → To 15.2 → To 37.2
- 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.Can you please help with the attached question? Thanks!(a) A hydrogen atom has its electron in the n = 6 level. The radius of the electron's orbit in the Bohr model is 1.905 nm. Find the de Broglie wavelength of the electron under these circumstances. m (b) What is the momentum, mv, of the electron in its orbit? kg-m/s