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Transcript
CHEM 141-01 Fall 2006 Quiz # 4 Name_______________________________ Use the following values in the problems if needed: c = 3.00 × 108 m/s (speed of light) h = 6.63 × 10–34 J·s (Plank’s constant) B = 2.18 × 10–18 J (Rydberg constant, a.k.a. RH) 1. (7 points) Find the frequency of light (in hertz, Hz) that has a wavelength of 566 nm. 566 nm = 566 × 10–9 m = 5.66 × 10–7 m ν= ν= 8 3.00 × 10 m / s 5.66 × 10 −7 m c λ = 5.30 × 1014 / s = 5.30 × 1014 Hz 2. (8 points) A photon has a wavelength of 624 nm. Calculate the energy of the photon in joules. E = hν = hc (6.63 × 10−34 J s)(3.00 × 108 m / s) = = 3.19 × 10−19 J − 9 λ 624 × 10 m 3. (7 points) Calculate the frequency (in Hz) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state. In this problem ni = 5 and nf = 3. ⎛ 1 1 ΔE = RH ⎜ − ⎜n2 nf 2 ⎝ i ⎞ ⎛ 1 1 ⎞ ⎟ = (2.18 × 10−18 J) ⎜ − = − 1.55 × 10−19 J 2 2 ⎟ ⎟ 3 ⎠ ⎝5 ⎠ The sign of ΔE means that this is energy associated with an emission process. Ephoton = hν and Ephoton = ΔEelectron thus, ΔEelectron = hν and ν= ΔE 1.55 × 10−19 J = = 2.34 × 1014 s −1 = 2.34 × 1014 Hz −34 6.63 ×10 J ⋅ s h 4. (7 points) An electron in a certain atom is in the n = 2 quantum level. List the possible values of l (and for each l list all values of ml ) that it can have. The angular momentum quantum number l can have integral (i.e. whole number) values from 0 to n − 1. In this case n = 2, so the allowed values of the angular momentum quantum number are 0 and 1. Each allowed value of the angular momentum quantum number labels a subshell. Within a given subshell (label l) there are 2l + 1 allowed energy states (orbitals) each labeled by a different value of the magnetic quantum number. The allowed values run from −l through 0 to +l (whole numbers only). For the subshell labeled by the angular momentum quantum number l = 1, the allowed values of the magnetic quantum number are −1, 0, and 1. For the other subshell in this problem labeled by the angular momentum quantum number l = 0, the allowed value of the magnetic quantum number is 0.
