From the information below, identify element X.

Question

a. The wavelength of the radio waves sent by an FM station
broadcasting at 97.1 MHz is 30.0 million (3.00 e7) times
greater than the wavelength corresponding to the energy difference
between a particular excited state of the hydrogen
atom and the ground state.

b. Let V represent the principal quantum number for the valence
shell of element X. If an electron in the hydrogen atom
falls from shell V to the inner shell corresponding to the excited
state mentioned above in part a, the wavelength of light
emitted is the same as the wavelength of an electron moving
at a speed of 570. m/s.

c. The number of unpaired electrons for element X in the ground
state is the same as the maximum number of electrons in an
atom that can have the quantum number designations n = 2,
mL = -1, and mS = -1/ 2.

d. Let A equal the charge of the stable ion that would form when
the undiscovered element 120 forms ionic compounds. This
value of A also represents the angular momentum quantum
number for the subshell containing the unpaired electron(s)
for element X.

All I know, or think I know, is:

C. n=2 means 2 possible subshells, mL=-1 means that L must ne 1 so it's a P subshell, so there are 6 electrons max so far, right?, but what about the ms=-1/2, what would that do?

I have no clue how to do a,b,d

Most of these railroad problems must be started at the top.
a. Change 97.1 MHz to wavelength.
speed of light = wavelength*frequency.
use speed of light in meters/second, wavelength will come out in meters, use frequency in Hz. Then divide that by 30,000,000 to obtain the wavelength of the line in the H spectrum.
Next, I would draw a diagram somthing like this.
N = ??______________
N=5 _______________

N=4 _______________

N=3 _______________

N=2 ________________

N=1 __________________

and calculate the energy of the electron in each of the first 5 or 6 orbits. (That's just a guess and the diagram above is not to scale).
E = -2.18E-18 J/N².
That is, plug in 1 squared for N = 1, 2 squared for N = 2, etc, and calculate energy for each level.

The difference between the energy of the orbits (the N values) will be the energy of the electron when it makes the transition between any one of them to any other below it. Convert energy difference to wavelength, delta E = hc/lambda and compare with the wavelength of the radio station divided by 30 million. That will tell you N for the excited state.

I hope this gets you started. Post any work if you need further assistance.

Answer 1

b. The wavelength of the electron moving at 570 m/s is the same as the wavelength of light emitted when the electron falls from shell V to the inner shell. Use the equation lambda = h/mv to calculate the wavelength of the electron. Then compare this wavelength to the wavelength of the radio station divided by 30 million. This will tell you the value of V.

c. The number of unpaired electrons for element X in the ground state is the same as the maximum number of electrons in an atom that can have the quantum number designations n = 2, mL = -1, and mS = -1/2. This means that the element X has two electrons in the n = 2 shell, one with mL = -1 and one with mS = -1/2.

d. Let A equal the charge of the stable ion that would form when the undiscovered element 120 forms ionic compounds. This value of A also represents the angular momentum quantum number for the subshell containing the unpaired electron(s) for element X. The angular momentum quantum number is related to the orbital angular momentum of the electron. The orbital angular momentum is related to the principal quantum number, n, and the angular momentum quantum number, l. Therefore, the angular momentum quantum number for the subshell containing the unpaired electron(s) for element X is equal to the principal quantum number, n.