Following are four possible transitions for a hydrogen atom. n₁ = 2; n₁ = 5 n₁ = 5; nf = 3 n₁ = 7; nf = 4 n₁ = 4; nf = 7 I. II. III. IV. (a) Which transition will emit the shortest wavelength photon? ---Select--- ✓ (b) For which transition will the atom gain the most energy? ---Select--- ✓ (c) For which transition(s) does the atom lose energy? (Select all that apply.) OI IV none
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- 3. Use the Rydberg formula to obtain the wavelength of the 80a radio line for an atom of infinite mass. Hence, taking the mass of the hydrogen nucleus to be 1836.1 electron masses, obtain the frequency of the 80a transition of atomic hydrogen. What resolving power would be required to separate the two transitions?5. The ground state energy for an electron in a hydrogen atom is -13.6 eV. What is the energy of the first excited energy state? A. -6.8 eV B. -9.6 eV C. -3.4 eV D. Oc) The electron in a hydrogen atom, originally in level n = 9undergoes a transition to a lower level by emitting a photon of wavelength 1821 nm. The final energy level is __________.
- 4. An electron in the n = 2 state of hydrogen is excited by absorbing the longest possible wavelength photon. What is the wavelength of this photon and what is its energy?Determine the wavelengths of the visible emission bands in the hydrogen spectrum arising from n2= 4, 5, and 6. A. 410 nm, 386nm, 340nm B. 486nm, 434nm, 410nm C. 1100nm, 486nm, 434nm D. 486nm, 434nm, 384nm E. 1260nm, 1100nm, 486nm5. A doubly ionized lithium atom is in the ground state. It absorbs energy and makes a transition to the n = 3 excited state. The ion returns to the ground state by emitting TWO photons ONLY. What is the wavelength of the lowest energy photon? m cei 16 c 16 cei the ploctron
- By developing the Schrodinger equation for the hydrogen atom determine: a. The probability of finding your electron in an orbit between [a0/2, 3a0/2] b. The probability of finding its electron inside the nucleus. c. The average radius of the electron's orbit.4. A particular atom has two energy levels with a transition wavelength of 420 nm. At 297 K there are 2.5 1021 atoms in the lower state. (a) How many atoms are in the upper state? (b) Suppose that 1.8 1021 of the atoms in the lower state are pumped to the upper state. How much energy could this system release in a single laser pulse?2. Consider an electron in a hydrogen atom that is transitioning from the n = 2 to the n = 6 level.What is the wavelength (in nm) of the photon associated with this transition?
- 1. The two prominent yellow lines in the spectrum of sodium result from transitions to the ground state from the 3p state with the electron spin-up, and from the 3p state with the electron spin-down. The wavelengths these two lines are 589.0 nm and 589.6 nm. (a) Calculate the energies in eV of the photons corresponding to these wavelengths, and the difference in energy of these photons AE. (b) The energy difference you found in part (a) is due to the spin-orbit effect. An electron in the 3p state of sodium experiences an internal magnetic field B, due to the orbital angular momentum. For a magnetic field B₁, the spin-orbit energy splitting is AE = 2µBB₁, where B is the Bohr magneton. Find the orbital magnetic field By from the energy difference AE you found in part (a).11. In the Balmer series, during which of the following energy state changes of the hydrogen atom is the photon with the most energy emitted? (A) n = 5 directly to n = 2 (B) n = 4 directly to n = 2 (C) n = 2 directly to n = 4 (D) n = 2 directly to n = 5 12. What is the minimum energy needed to ionize a hydrogen atom when it is in the n = 2 state? (A) 1.9 eV (B) 3.4 eV (C) 12.2 eV (D) 13.6 eV4. Describe the following energy state transition for an electron in a hydrogen atom. List the energy of the emitted photon, wavelength, its initial and final orbit. (a) n=3 to n = 1, (b) n=6 to n= 2, (c) n = 5 to n=3.