Can someone explain how to do this?
1B.7 Sodium vapor lamps, used for public lighting, emit yellow light of wavelength 589 nm. How much energy is emitted by (a) an excited sodium atom when it generates a photon; (b) 5.00 mg of sodium atoms emitting light at this wavelength; (c) 1.00 mol of sodium atoms emitting light at this wavelength?
Textbook problem B.7
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Audra Mcleod 3G
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Re: Textbook problem B.7
Hello!
a) So to determine the energy of an excited sodium atom, you would first use the wavelength to determine the frequency of the light emitted through the equation speed of light =(wavelength)(frequency). This would give you 5.093 x 10^14 (3.0x10^8/589x10^-9). You would then use this frequency in the equation E = hv, which would give you a final answer of 3.37 x 10^-19 J (6.626x10^-34 x 5.093x10^14).
b) For the energy of 5.00 mg, you would have to convert this value to the number of sodium atoms, and multiply by the energy per atom you calculated in a). This conversion would look like this:
5 mg/1 x 1 g/ 1000 mg x 1 mol/ 22.99 g x 6.022x10^23 atoms/ 1 mol = 1.3097 x 10^20 atoms x 3.37x10^-19 = 44.1 J
c) For this problem, it is the same method in b), except you don't have to convert to number of atoms because you already know there is 6.022x10^23 atoms in 1 mole. So you would simply do (6.022x10^23)(3.37x106-19)= 202,941.4 J, but since the numbers given in the problem only has 3 sig figs you would round this number to 203,000 J or 203 kj.
Hope this helps!
a) So to determine the energy of an excited sodium atom, you would first use the wavelength to determine the frequency of the light emitted through the equation speed of light =(wavelength)(frequency). This would give you 5.093 x 10^14 (3.0x10^8/589x10^-9). You would then use this frequency in the equation E = hv, which would give you a final answer of 3.37 x 10^-19 J (6.626x10^-34 x 5.093x10^14).
b) For the energy of 5.00 mg, you would have to convert this value to the number of sodium atoms, and multiply by the energy per atom you calculated in a). This conversion would look like this:
5 mg/1 x 1 g/ 1000 mg x 1 mol/ 22.99 g x 6.022x10^23 atoms/ 1 mol = 1.3097 x 10^20 atoms x 3.37x10^-19 = 44.1 J
c) For this problem, it is the same method in b), except you don't have to convert to number of atoms because you already know there is 6.022x10^23 atoms in 1 mole. So you would simply do (6.022x10^23)(3.37x106-19)= 202,941.4 J, but since the numbers given in the problem only has 3 sig figs you would round this number to 203,000 J or 203 kj.
Hope this helps!
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Ryan_Page_1J
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