Physics

Problem

An electron in an atom transitions from an energy level at

-2.0\,\text{eV}

to a lower level at

-5.0\,\text{eV}

. Calculate the wavelength of the photon that is emitted, in nanometres. Express your answer to two significant figures. Constants:

h = 6.63\times10^{-34}\,\text{J}\cdot\text{s}

c = 3.00\times10^{8}\,\text{m/s}

1\,\text{eV} = 1.60\times10^{-19}\,\text{J}

Intuitive explanation

When an electron drops to a lower energy level, it releases the energy difference as a photon. The key is to find that energy gap (which is always positive when going downward), convert it to joules, then use the relationship $E = hf$ and $c = \lambda f$ to connect energy directly to wavelength via $\lambda = \frac{hc}{E}$ . Watch the signs carefully—the energy released is what matters for the photon.

Intuitive explanation

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