13. (a) Find the higest energy of the photon emitted by a downward electron transition in the Paschen series?
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- 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?3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction e 2ao, where a, is the Bohr radius. 1 is (2ао)3/2 VЗа. (а) What possible angles might the angular momentum vector L make with the Z-axis? (b) What is the most probable radius (in terms of a.) at which the electron is found? (c) What is the expectation value of r in this state? Note: S xe-"dx 120. (d) What is the probability of finding such an electron between a, and ∞? Note: ° x*e-"dx = 23.91.The L series of the characteristic x-ray spectrum of tungsten contains wavelengths of 0.1099 nm and 0.1282 nm. The L-shell ionization energy is 11.544 keV. Which x-ray wavelength corresponds to an N → L transition? Determine the ionization energies of the M and N shells: If the incident electrons were accelerated through a 40.00 keV potential difference before striking the target, find the shortest wavelength of the emitted radiation:
- Please answer (i), (v), and (vi). Thank you! (i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in the actual number with the unit of [eV]. We consider a transition that electron in the 3p state emits a photon and make a transition to the 2s state. What is the frequency v of this photon ? (ii) Now we do not include electron spin angular momentum, and just estimate an effect of a magnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum. How many lines of optical transition do we expect ? What is the interval of the frequency in the field B = 0.1 Tesla ? (iii) In this situation, we do not expect transition from 3s to 2s state if the electron is initially in the 3s state, Explain the reason. (iv) We now consider an effect of magnetic field B to a free electron spin (not in Hydrogen, but a free electron). The magnetic field of B = 1.0 Tesla will split the energy level into two (Zeeman) levels. Obtain the level…Determine the wavelength if the electron is excited n=2 for Helium (Z=2).( E=(-13.6ev)Z2/n2 and 1/mu=1/hc(En-En-1)