Q18 of 43 Page 407

Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).

we know the relation between energy and momentum P of a electromagnetic radiation having velocity C and energy E is


P = E/C


and we know energy of electromagnetic radiation is given by relation


E = h

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17

For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10–10m?

 17

Also find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of (3/2) k T at 300 K.

 19

What is the de Broglie wavelength of a nitrogen molecule in air at 300 K? Assume that the molecule is moving with the root mean square speed of molecules at this temperature. (Atomic mass of nitrogen = 14.0076 u)

 20

(a) Estimate the speed with which electrons emitted from a heated emitter of an evacuated tube impinge on the collector maintained at a potential difference of 500 V with respect to the emitter.

Ignore the small initial speeds of the electrons. The specific charge of the electron, i.e., its e/m is given to be 1.76 × 1011 C kg–1.


(b) Use the same formula you employ in (a) to obtain electron speed for a collector potential of 10 MV. Do you see what is wrong? In what way is the formula to be modified?