Electricity and Magnetism
# E+M Warmups

In atoms, electrons jump between energy levels, and they absorb or radiate energy in the form of light (photons). An electron falls to a lower energy level when it radiates a photon, and jumps to a higher energy level when it absorbs a photon.

Find the wavelength of the photon that radiates when an electron jumps from the $n = 3$ energy level down to the $n = 2$ energy level. Where is this photon in the electromagnetic spectrum?

**Assumptions**

- $h$ (Planck's constant) = $4.14 \times 10^-15$ eV s.
- $c$ (Speed of light) = $3 \times 10^8$ m/s.
- All values are approximate.
- Assume that this is a hydrogen atom.

$\lambda.$ Let this wire be on the $y$-axis of the $xy$-plane, and let $x > 0$ be the distance between the $y$-axis and a point $P$ on the $xy$-plane. What is the strength of the electric field at the point $P?$

Suppose that an infinitely long straight current-carrying wire has a uniform linear charge densityNote: $\epsilon_0$ in the choices below denotes the electric constant.

$100 \text{ V}$. It then has a de Broglie wavelength of $x_1$.

An electron, practically at rest is initially accelerated through a potential differenceIt then gets retarded through $19 \text{ V}$ and has a wavelength of $x_2$.

A final retardation through $32 \text{ V}$ changes the wavelength to $x_3$.

What is $\displaystyle\frac{x_3-x_2}{x_1}$ as a percentage?