How does the distance between adjacent orbits in a hydrogen atom vary with increasing values of the orbital number n? What should take place for a hydrogen atom to emit longest possible wavelength in Balmer series? Explain.
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- The wavelengths of the Brackett series for hydrogen are given by n = 5, 6, 7,.... (a) What are the wavelengths of the first three spectral emission lines in this series (in nm)? (Enter them in order of decreasing wavelength.) largest value nm nm smallest value nm (b) In which band of the electromagnetic spectrum do these lines appear? visible light region O infrared region O ultraviolet region O gamma ray region O x-ray region3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction is (2a.)3/2 /3a. 2ao , where a, is the Bohr radius. (a) 2-axis? What possible angles might the angular momentum vector L make with the (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: xe-"dx = 120. (p) S° x*e-dx = 23.91. What is the probability of finding such an electron between a, and oo? Note: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.
- please help as soon as possiblePlease 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…The Balmer series in hydrogen includes the Paschen series. has four lines in the ultraviolet. O includes both the Paschen series and the Lyman series. O has four lines in the visible. O includes the Lyman series.
- An electron is in the third excited orbit of hydrogen, corresponding to n = 4. (a) Find the radius of the orbit. nm (b) Find the wavelength of the electron in this orbit. nmThe Balmer series in the hydrogen emission spectrum is formed by electron transitions from nj> 2 to nf= 2. What is the longest wavelength in the Balmer series? nmA hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.