From the information, what is element X ? a.) The wavelength of the radio waves
ID: 545757 • Letter: F
Question
From the information, what is element X?
a.) The wavelength of the radio waves sent by an FM station broadcasting at 97.1 MHz is 30.0 million (3.00 x 10^7) times greater than the wavelength corresponding to the energy difference between a particular excite stateof the hydrogen atom and the ground state.
b.) Let V represent the principle 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 principle quantum number for the lowest energy excited state for hydrogen. The value of A also represents the angular momentum quantum number for the subshell containing the unpaired electron(s) for element X.
Explanation / Answer
We know,
Where = wavelength, c =speed of light and = frequency
=1.02 *10-8 m
Let the transition be from n=1 to n=n, we know that
Putting the values we get,
(1/1.02 *10-8)= 1.096*107 (1/n2-1)
Solving for n we get n= 3. Therefore, the transition is from n=3 to n=1
where h is Plank’s constant
Putting the values we get,
= 1.277 *10-6 m
This transition is from shell V to 3
Therefore,
1/1.277 *10-6 = 1.096*107 (1/V2-1/32)
Which gives V= 2
ml = -l, -(l-1),….
For l= 1, we get ml= -1 which suggests p orbital. The principal quantum number is 2.
So, the electronic configuration is 1s2 2s2 2p1
Hence the element X is Boron (B)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.