Three mono-energetic beams

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

Problem

Three mono-energetic beams, each consisting of a different charged particle, are produced as follows: • Beam A: electrons are accelerated from rest through a potential difference of

20\,{\rm V}

. • Beam B: protons are accelerated from rest through the same potential difference of

20\,{\rm V}

. • Beam C: alpha particles (charge

+2e

, mass

4m_{\text{p}}

) are accelerated from rest through the same potential difference of

20\,{\rm V}

. (i) Show that the kinetic energy gained by a particle of charge

q

when accelerated through a potential difference

V

qV

. (ii) Derive an expression for the wavelength of a particle of mass

m

and charge

q

accelerated through

V

. (iii) Hence obtain the ratio of the wavelengths

\lambda_\text{A} : \lambda_\text{B} : \lambda_\text{C}

for the three beams. (iv) State which beam will exhibit the most pronounced diffraction effects when passed through a narrow slit and justify your answer.

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