Question

Derive the relationship for the momentum (p) of a relativistic mass bearing particle: p = (1/c)*[E_T² – E₀²]^0.5 and then, via De-Broglie’s hypothesis, derive the expression for the associated
wavelength

Answer 1

The espression for tatal Energy is given as, E = mc² i VI-V2/2 and, Exepression for momentum, p = mv ti) Sqlasing eg" and Lii) E² - mèch (1-v2, (2) p² - m² u 2 liv (1-43,2) multiplying ean civ) by c ² on both side, p2 c ² – m2, 2 c² (1-12 (2) substracting egn (V) from (iii) E²-p2 c ² = mach – m² 2 2 (1-v3²) (1-v2/(?)

E- p2c2 - m?c4( ! -v%C2) (1-1²/ 2) E²-p2 c ² = m²c4 (1-12/ (2) (1-12 (2) cancelling tesim (-v2/c2) from both numerator y and denominator. Dis | E- Pºcº = mc sowing for momentum ; – p2c2 = mech – E² - p2c2 - - Em2 c4 +) p2 c 2 = (E² m2 (4) p2 = (E- me") PEVA E? m?cs) | b = 1 (E? _ m2.4) 2

energy p= (E? - n1c7) where, me? = Ep + Called Rest mass E is tatal energy .. E=E.. P= + [- (mc2)2]” Tp- & [ { - E?] ² proueds for associated wavelength : 2 . using de-Broglie hypothesis. a = ! i where 27 wavelength h → Planck's constant → momentum plugging the value of p. ... bi 2= TE Eye & up Expression for associated Wanelongti.
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