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(1) Black-body radiation To prove the Wien's Law : max T constant d ( ) d let x 6 h c / kT 1) 1 5 (e h c / kT 1) 2 e h c / kT max 5 (e max kT hc 1 x hc2 kT max 0 we have : 1 x 5 x(e 1) e 0 by u sin g Newton' s method, we obtain : x 0.2014052 max T 0.00289779mK (2) The Uncertainty principle (melons in quantum land) (a) Why do we have to be careful when cutting open melons grown in quantum land ? x Px V x h 4 h , m 0.0001kg, x 0.2m, 4 m x V x 25 m / s Very fast ! The seeds leave the melon with this velocity when it is cut open. So you should be careful. (b) Are such melons visible? No, Let's consider the recoil of a melon at reflection of a "visual" photon. Because the peel of the melons is very hard, the collision can be treated as elastic collision, then the momentum of the melon after the collision is approximately : PM 2 Pphoton h 10 4 kg m / s v 5 km / s very fast By the time this photon is seen, the melon is already situated elsewhere