Practice portal › Dual Nature of Matter and Radiation › de Broglie Wavelength and Accelerating Potential

A particle of mass m kg and charge q coulomb is accelerated through V volt. The de Broglie wavelength associated with it is ______.

Asked in GUJCET 2013 · Accelerated through a potential difference

• (1) (hq)/(√2mV)
• (2) h/(√mqV)
• (3) h/(√2Vqm)
• (4) h/(√mV)

Step-by-step solution

Why the other options are wrong

• (1) The charge has been lifted out of the root and put in the numerator. The charge enters only through the energy qV inside p = √2mqV, so it can appear only as √q in the denominator. A factor q on top would also make the wavelength grow with charge, when a bigger charge is accelerated harder and so has a shorter wavelength.
• (2) The factor 2 has been dropped. It comes from K = (p²)/(2m), which gives p = √2mK; leaving it out makes the wavelength √2 times too large.
• (4) Both the 2 and the charge have been dropped, as though the energy gained were V itself. A charge q falling through V volt gains qV joule of kinetic energy, not V joule, so q must stay under the root.

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