Determine the initial and final values of n associated with this emission
Please tell me how you got your answer
Please tell me how you got your answer
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Your textbook probably contains a table that gives the basic structure of the hydrogen atom in terms of the number of electron-volts needed to ionize the atom. In such a table, the "ground state" where n=1 is associated with the energy level -13.6 eV, the n=2 state is associated with energy of -3.4 eV, and so on. If such a table doesn't appear in your textbook, Google "energy levels of H atom," and you'll find several possibilities.
Now, how to relate this to wavelength? The energy of a photon is given by E = hc/lambda, where h is Planck's constant, c is the speed of light, and lambda is the wavelength of the photon. Since the table of energies that I'm working gives them in eV, I'm going with Planck's constant expressed in electron-volt seconds:
h = 4.13567*10^(-15) eV*s
c = 2.998 * 10^(8) m/s
If we are given lambda = 93.0 nm = 93.0*10^(-9) m,
then E = (4.13567*2.998/93.0)*10^(2) eV = 13.33 eV
This is a large amount of energy, too large to be emitted in any transition that would end up at n=2; it must be a transition from n=7 to n=1, corresponding to (-0.278 eV - (-13.6 eV)). The reason we know that the initial state is the n=7 and final state n=1 instead of the other way around is that an "emission" means the atom gave off energy and ended up at a lower energy level, whereas "absorption" of radiation would be associated with an increase in the atom's energy level.
Now, how to relate this to wavelength? The energy of a photon is given by E = hc/lambda, where h is Planck's constant, c is the speed of light, and lambda is the wavelength of the photon. Since the table of energies that I'm working gives them in eV, I'm going with Planck's constant expressed in electron-volt seconds:
h = 4.13567*10^(-15) eV*s
c = 2.998 * 10^(8) m/s
If we are given lambda = 93.0 nm = 93.0*10^(-9) m,
then E = (4.13567*2.998/93.0)*10^(2) eV = 13.33 eV
This is a large amount of energy, too large to be emitted in any transition that would end up at n=2; it must be a transition from n=7 to n=1, corresponding to (-0.278 eV - (-13.6 eV)). The reason we know that the initial state is the n=7 and final state n=1 instead of the other way around is that an "emission" means the atom gave off energy and ended up at a lower energy level, whereas "absorption" of radiation would be associated with an increase in the atom's energy level.