2.) Bohr Model for the Hydrogen Atom The energy levels available to the electron in hydrogen are given by the following equation: E₁ == RH 2 n where, R₁ = 2.179 x 10¹8 J and n= 1, 2, ..., ∞, (a) Calculate the difference in energy (in J) between an electron in n = 1 and an electron in n=3.
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- 2 R --- n multiple choice question In the equation below, the Balmer series involves the emission lines (wavelengths) obtained when electrons go from any higher energy (excited) level to A The ground level (n = 1) B. The first atomic level (n = 2) C. The third atomic level (n = 3) D. The fourth atomic level (n = 4) Jump to E. The fifth atomic level (n = 4) 2 where, R = 1.097 x 107 m1 3 53 Spectroscopy Light can be emitted and absorbed by atoms, but only when the energy of the light, E = hf, matches the energy difference of two allowed states of an atom. For the transition m →n, the energy difference is AE = Em - En. Thus, light will be emitted or absorbed only if hf = En-Em- In the Bohr model of hydrogen, the energy of the n-th electron orbit is En -13.6 eV n² (a) Transitions of the form m → 1 make up the Lyman series of spectral lines. Calculate the wavelengths of the first 3 lines in the Lyman series. In what region of the electromagnetic spectrum do these lines appear? (b) Transitions of the form m → 2 make up the Balmer series of spectral lines. Calculate the wavelengths of the first 3 lines in the Balmer series. In what region of the electromagnetic spectrum do these lines appear? (c) Transitions of the form m → 3 make up the Paschen series of spectral lines. Calculate the wavelengths of the first 3 lines in the Paschen series. In what region of the…QUESTION 8 An electron in hydrogen absorbs a photon and jumps from orbit n = 2 to n = 4. Using the energy level diagram shown, what was the energy of the absorbed photon? a. 0 eV b. 0.85 eV c. 3.4 eV d. 10.2 eV e. 2.55 eV
- 51) A photon of energy 1.24 eV is absorbed by a molecule. a) What is its wavelength in cm and the reciprocal of its wavelength in cm-1? A..........cm B..........cm-1 The molecule transitions to an energy level of 0.24 eV, and emits a photon. b) What is the energy of the emitted photon (eV)? ..........eV c) What is its wavelength in cm and the reciprocal of its wavelength in cm-1? C..........cm D..........cm-1 d) Find D-B in cm-1. ..........cm-1 The second photon of energy 1.14 eV is absorbed by the same molecule. e) What is its wavelength in cm and the reciprocal of its wavelength in cm-1? E..........cm F..........cm-1 The molecule transitions to an energy level of 0.24 eV, and emits a photon. f) What is the energy of the emitted photon (eV)? ..........eV g) What is its wavelength in cm and the reciprocal of its wavelength in cm-1? G..........cm…6) Which of the following are possible values for the constantni in the hydrogenspectrum, given the lines are in thePaschen series? A)0,±1,±2,±3,... B)±1,±2,±3,... C)0,1,2,3,... D)2,3,4,5,... E)4,5,6,7,... 7) The symbol Z is used in the Bohr calculations. What does it represent? A) the number of nucleons (neutrons and protons) in an atom’s nucleus B) the number of protons in an atom’s nucleus C) the number of neutrons in an atom’s nucleus D) the number of electrons in an atom’s nucleus E) the mass of an atom’s nucleusQuestion in images
- 1. Differentiate the three quantum numbers for an electron in the hydrogen atom and justify why the idea of an electron orbiting a proton has been abandoned.3. A hydrogen discharge tube is operated at about 300 K in the laboratory. Compute the ratio of the probability for spontaneous emission to the probability for stimulated emission of the first Balmer line (the transition from the n = 3 state to the n = 2 state of the hydrogen atom).