In what year did Planck publish his famous equation? O 1936 O 1900 O 1905 O 1912

Imagine an alternate universe where the value of the Planck constant is 6.62607x10−36J·s. In that universe, which of the following objects would require quantum mechanics to describe, that is, would show both particle and wave properties? Which objects would act like everyday objects, and be adequately described by classical mechanics? A buckyball with a mass of 1.2 x 10-21 g, 0.7 nm wide, moving at 11. m/s. An iceberg with a mass of 2.2 x 108 kg, 70. m wide, moving at 1.43 km/h. A mosquito with a mass of 1.1 mg, 8.2 mm long, moving at 1.2 m/s A bacterium with a mass of 5.0 pg, 9.0 µm long, moving at 1.00 µm/s.

If you double the temperature of a blackbody, by what factor will the total energy radiated per second per square meter increase?

4. A particle of mass, m, is placed in a 1D-box of length, a, for which it is confined to be within the range 0 < x < a. Just after a measurement of some kind, where the system interacts with a measuring device, the final state of the system is given as (x, t = 0*) = c(e-ic 2(x) + vZe-i83(x) – $4(x)) where (dn} defines a complete set of orthonormal wave functions that solves the TISE, and a = and & = . If many experiments are performed that measure the energy on identically prepared systems, it is possible to quantify the statistical properties of possible outcomes. Answer the following questions. Part (e) is tedious and a bit time consuming. What does this integral o P¿(x) ¢n(x) dx equal to? What is the normalization constant. What is the probability for the particle to be measured in energy state n? What is the predicted average energy from many measurements of energy?