### Lunar Leaper

Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?

### Which Twin Is Older?

A simplified account of special relativity and the twins paradox.

### Whoosh

A ball whooshes down a slide and hits another ball which flies off the slide horizontally as a projectile. How far does it go?

# Levels of Bohr

##### Stage: 5 Challenge Level:

The energy levels of the electrons in a hydrogen atom according to the Bohr model are given by

$$E_n = -\frac{m_ee^4}{8\epsilon_0^2h^2n^2}\, n=1, 2, 3, \dots$$
where $m_e$ and $e$ are the mass and charge of the electron, $h$ is Planck's constant and $\epsilon_0$ the permittivity of free space.

This expression draws together many the fundamental constants involved in quantum mechanics. What are all of the S.I. units of these constants?

Using just these constants is it possible to create a dimensionless quantity?

Can you make a quantity with dimensions $[L]$ (length) or $[T]$ (time) using these quantities?