Three separate beams are produced as follows: • Beam A: Electrons accelerated from…

PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation

Problem

Three separate beams are produced as follows: • Beam A: Electrons accelerated from rest through

500\,\text{V}

. • Beam B: Protons accelerated from rest through

10\,\text{kV}

. • Beam C: Doubly–ionised helium nuclei (alpha particles) accelerated from rest through

15\,\text{kV}

. (i) For each beam, write an expression for the de Broglie wavelength in terms of the given accelerating potential, indicating all parameters involved. (ii) Using

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

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

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

and

e = 1.6\times10^{-19}\,\text{C}

, calculate the numerical value of the wavelength for each beam. (iii) Rank the three beams in order of increasing de Broglie wavelength and explain the underlying physical reason for the ordering obtained.

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