The following values are the only allowable energy levels of...

The following values are the only allowable energy levels of a hypothetical one-electron atom: E6 = -2 X 10^-19 J E5 = -7 X 10^-19 J E4 = -11 X 10^-19 J E3 = -15 X 10^-19 J E2 = -17 X 10^-19 J E1 = -20 X 10^-19 J A) If the electron were in the n = 3 level, what would be the highest frequency (and minimum wavelength) of radiation that could be emitted? B) What is the ionization energy (in kJ/mol) of the atom in its ground state? C) If the electron were in the n = 4 level, what would be the shortest wavelength (in nm) of radiation that could be absorbed without causing ionization?

Transcript

00:01 So we have a series of energy levels for a hypothetical one electron atom, and the lowest energy level is negative 20 times 10 to the negative 19th joules.

00:13 And the second lowest, we're told, is negative 17.

00:18 So negative 17 times 10 to the negative 19th joules.

00:23 The third is negative 15 times 10 to the negative 19th jewels.

00:29 Our fourth level is going to be 13, and then fifth and sixth are 7 and negative 2.

00:38 So this is negative 13 times 10 to the negative 19th jules.

00:43 Then we have two more.

00:45 So this will be negative 7 times 10 to the negative 19th joules.

00:49 And then the last one, presumably it's a negative number.

00:53 It says plus 2, but i think really what that would mean is negative 2.

00:55 Because energy levels are always going to be negative for a bound state.

01:00 So it should be negative.

01:01 Anyway, so the first question asks, if the electron is in the n -equals -3 level, what would be the highest frequency and minimum wavelength of radiation that can be emitted? so the highest frequency occurs when the energy difference is for the largest energy difference.

01:20 And so the largest energy difference that occurs if we're in the n -equals -3 state, would be like going from the three to the sixth state because that's a energy difference of like 13 times 10 to the 10 to the negative 19th so let's write that our energy difference our largest energy difference is going to be this and so our frequency is going to be this energy difference divided by planx constant so if you do that 13 times 10 to the negative 19th divided by 6 .63 times since the negative 34th we get a frequency of about 1 .96 times 10 to the 15th hertz.

02:06 That's our largest frequency.

02:08 And then, of course, you can find the wavelength.

02:11 There we go.

02:12 My eraser wasn't working.

02:13 We can find the wavelength by just dividing the speed of light by this frequency.

02:19 So if we do that, we get something like 1 .53 times 10 to the negative 7 meters, or 153 nanometers.

02:29 Next up, we want to know what is the ionization energy of the atom in its ground state? so this would represent basically the biggest energy difference overall.

02:40 If these are our six energy levels, then the ground state energy or the ionization energy would be the energy required to go from the lowest state out of the atom, basically.

02:54 So presumably it's the ionization energy, we'll call us like e .n.

02:57 Or something...

Question

Please give Ace some feedback