Question

select the false statement
an electron in the n = 5 level is higher in energy than an electron in an n = 3 level.
for an electron to transition from the n = 5 level to the n = 3 level it must gain energy.
when an electron transitions from the n = 5 level to the n = 3 level a photon of light is emitted.

Explanation:

• The energy of an electron in a hydrogen - like atom is given by \(E =-\frac{13.6}{n^{2}}\text{ eV}\). As \(n\) increases, the magnitude of \(E\) decreases (but since it is negative, the energy of the electron increases). So, an electron in \(n = 5\) is higher in energy than an electron in \(n=3\).
• When an electron transitions from a higher energy level (\(n = 5\)) to a lower energy level (\(n = 3\)), it loses energy. The energy difference \(\Delta E=E_{5}-E_{3}\) is released in the form of a photon. The formula for the energy of a photon is \(E = h

u\), where \(h\) is Planck's constant and \(
u\) is the frequency of the photon.

Answer:

The false statement is: For an electron to transition from the \(n = 5\) level to the \(n = 3\) level it must gain energy.