Physics

Problem

An electron, a neutron and a doubly–ionised helium nucleus (alpha particle) are each given the same kinetic energy of

1.5\,\text{keV}

. a. (i) Derive an expression for the de Broglie wavelength

\lambda

of a non–relativistic particle in terms of its mass

m

and kinetic energy

E_k

. b. (ii) Using

m_e = 9.1\times10^{-31}\,\text{kg}

m_n = 1.67\times10^{-27}\,\text{kg}

and

m_\alpha = 6.64\times10^{-27}\,\text{kg}

, calculate the wavelength for each particle and arrange them in ascending order of wavelength (smallest to largest).