suppose a particular atom has only two allowable electron orbits. how many different wavelength photons (spectral lines) would result from all electron transitions in this atom?
1. three
2. four
3. None of these
4. one
5. two
please help..
Since a photon results from a transition from one orbit to one of a lower energy, I do not see how more than one transition would be possible with a photon resulting.
For an atom with only two allowable electron orbits, the number of different wavelength photons (spectral lines) resulting from all electron transitions is given by the formula:
n = (n^2 - n) / 2
Where 'n' is the number of allowable electron orbits.
In this case, n = 2.
Plugging in the value, we get:
n = (2^2 - 2) / 2
n = (4 - 2) / 2
n = 2 / 2
n = 1
Therefore, there would be only one different wavelength photon (spectral line) resulting from all electron transitions in this atom.
So, the correct answer is option 4.
To determine the number of different wavelength photons resulting from all electron transitions in an atom with only two allowable electron orbits, we need to consider the possible transitions between these orbits.
In general, the number of different electron transitions in an atom is given by the combination formula, which is given by:
C(n, 2) = n! / (2!(n-2)!),
where n is the total number of allowable electron orbits.
In this case, since the atom has only two allowable electron orbits, we substitute n = 2 into the equation:
C(2, 2) = 2! / (2!(2-2)!) = 1.
Therefore, there is only one possible transition between these two orbits. As a result, there would be one different wavelength photon (spectral line) resulting from all electron transitions in this atom.
So, the correct answer is option 4. one.