An electron undergoes a transition from an n=3 to an n=1 stationary state and red light is released.
Which of the following forms of electromagnetic radiation could be released for an n=2 to n=1 electron transition within the same atom?
-blue visible light
-yellow visible light
-radio wave radiation
-ultra violet radiation
Here is a diagram that should help answer this question.
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To determine which form of electromagnetic radiation could be released for an n=2 to n=1 electron transition within the same atom, we need to consider the energy difference between these two states.
The energy of an electron in a stationary state is given by the equation:
E = -13.6 eV / n^2
where E is the energy of the electron and n is the principal quantum number.
For an electron transitioning from n=2 to n=1, we can calculate the energy difference as:
ΔE = E(initial) - E(final)
= (-13.6 eV / 2^2) - (-13.6 eV / 1^2)
= -13.6 eV / 4 + 13.6 eV
= -3.4 eV + 13.6 eV
= 10.2 eV
Now, we can compare this energy difference to the energy associated with each form of electromagnetic radiation.
The energy of a photon is given by the equation:
E = hc / λ
where E is the energy of the photon, h is Planck's constant (6.63 x 10^-34 J*s), c is the speed of light (3.0 x 10^8 m/s), and λ is the wavelength of the radiation.
Radio wave radiation, with the longest wavelength, has the least energy among the options provided. Therefore, it is unlikely that radio wave radiation could be released for this transition since the energy difference is 10.2 eV.
Ultra violet radiation, with shorter wavelengths, has higher energy. However, the energy difference of 10.2 eV is still much lower than that associated with ultra violet radiation, which typically ranges from 3 to 124 eV. Therefore, ultra violet radiation is also unlikely to be released for this transition.
Blue visible light and yellow visible light fall within the range of energies that could be released for a transition of 10.2 eV. However, we need to compare the energies of each respective colors of light to the calculated energy difference.
Blue visible light has a higher energy compared to yellow visible light. Blue light typically has an energy range of 2.0 to 2.8 eV, while yellow light usually falls within the range of 1.8 to 2.2 eV.
Since the calculated energy difference of 10.2 eV is closer to the energy associated with blue visible light, it is more likely that blue visible light could be released for an n=2 to n=1 electron transition within the same atom.