A student analyses a log–log graph of the de Broglie wavelength (vertical axis)…

PHYSICS · Subjective · A Level · Physics · Particles and radiation · Particles and radiation

Problem

A student analyses a log–log graph of the de Broglie wavelength

\lambda

(vertical axis) versus the speed

v

(horizontal axis) for a non-relativistic particle of unknown mass. (a) Derive the theoretical relation between

\lambda

and

v

and hence obtain the expected slope of a

\log_{10}(\lambda)

versus

\log_{10}(v)

plot. (b) The experiment yields a slope of

-0.98

and shows that when

v = 1.5\times10^{6}\,\text{m\,s}^{-1}

the corresponding wavelength is

\lambda = 5.0\times10^{-10}\,\text{m}

. Using these two pieces of information, determine the mass of the particle. (c) Identify the particle by comparing your calculated mass with standard sub-atomic particle masses.

Related theory

Matter Waves
Dual Nature of Radiation and Matter
Wave nature of matter
Wave particle duality

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