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.

Suppose that an infinitely long straight current-carrying wire has a uniform linear charge density \(\lambda.\) 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 \(P?\)

Note: \(\epsilon_0 \) in the choices below denotes the electric constant.

An electron, practically at rest is initially accelerated through a potential difference \(100 \text{ V}\). It then has a de Broglie wavelength of \(x_1\).

It 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?

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