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CHM 111 Chapter 7 Worksheet: The Quantum mechanical model of an atom Name: _________________________________ Q1. The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of 589 nm. (A) What is the frequency of the radiation? 5.09 × 1014 1/s (B) What is the energy of a photon of this light? 3.37 × 10-19 J (C) What is the energy of 1.00 mole of photons of this frequency? 203000 J or 203 kJ Q2. Arrange the following regions of the electromagnetic spectrum in order of increasing frequency Microwave, X Rays, Ultraviolet, Visible, Gamma rays Microwave, Visible, Ultraviolet, X rays, Gamma rays Q3. What does it mean when we say that light is quantized? It exists as a bunch of photons, or individual packets of light. One photon is the smallest amount of light you can have, and you can’t divide it any further. Light is always a whole number, or quantity, of photons, and fractions are impossible, so light is “quantized”. (This isn’t quite the normal definition of “quantity”, but no one could come up with a better word for this idea, so we’re stuck with “quantized”. This is also where the word “quantum” comes from.) Q4. What is the difference between a line spectrum and a continuous spectrum? A continuous spectrum has light of essentially every color and wavelength, without any gaps (put through a prism, it looks like a full rainbow). A line spectrum contains only a handful of very specific colors or wavelengths, and every other color is missing; it’s mostly gaps (put through a prism, you might see a narrow slice of blue, a narrow slice of green, and a couple narrow slices of red, and all the other colors are missing). Q5. Give the maximum number of orbitals in an atom that can have these quantum numbers: (A) n = 3 _____9________ (B) n = 3, l = 1 _____3________ (C) n=2, l=1, ml= 0 _____1_________ (D) n=0, l=0, ml=0 _____0_________ Q6. Removing the electron from a Hydrogen atom corresponds to a raising the electron from n=1 to an orbit that has n=∞. What is the energy needed to remove the electron from a hydrogen atom? 2.18 × 10-18 J What is the energy in terms of kJ per mole? 1310 kJ/mol or 1.31 × 103 kJ/mol Q7. The light from a Helium-Neon laser (used to define a meter) has a wavelength of 632.99139822 nm Calculate the frequency of this laser beam. 4.736 × 1014 1/s What is the energy of one mole of this radiation? 1.89 × 105 J or 189 kJ Q8. Calculate the velocity of an electron that has a de Broglie wavelength of 0.0897 nm. Mass of an electron = 9.11 10-28 g 8.11 × 106 m/s Q9. Circle the sets of quantum numbers that can specify an orbital. a) n = 3, l = 3, ml = 0 b) n = 1, l = 0, ml = 0 c) n = 5, l = 4, ml = -4 d) n = 2, l = 2, ml = -2 Q10. One photon of a particular radiation has energy of 6.22 10-19 J. a) Calculate the frequency of this radiation. 9.39 × 1014 1/s b) What is the wavelength of this radiation in nm? 320 nm Q11. Consider the transition from n = 1 to n = 5 in the Hydrogen atom. a) Is energy absorbed or emitted in this transition? absorbed b) Calculate the energy of the photon that corresponds to this transition. 2.09 × 10−18 J c) Calculate the wavelength that corresponds to this transition. 9.49 × 10−8 m or 94.9 nm Q12. Circle each of the following orbitals that are real (can exist). a) 2d b) 3f c) 1s d) 3d e) 6p Q13. The brightest light emitted by the sun has a wavelength of about 0.48 µm. Calculate the frequency of this radiation. 6.2 × 1014 1/s What is the energy of one photon of this radiation? 4.14 × 10−19 J Q14. Q15. What is the maximum number of orbitals that are specified by each set of quantum numbers? a) n=3, l=2, ml = -2 1 b) n=1, l=0 1 c) n=5 25 d) n=2, l=2 0 e) n=5, l=3 7 f) n = 2 4 Arrange the following colors of the visible light in order of increasing wavelength. Orange, Blue, Green, Violet, Yellow, Red Violet, Blue, Green, Yellow, Orange, Red Q16. An object weighing 0.100 g is travelling at a speed of 45.0 m/s. What is the deBroglie wavelength of this object? 1.47 × 10−31 m