HW #1 1.1 Summarize the evidence that led to the introduction of quantum mechanics. 【 】 1.2 Calculate the size of the quantum involved in the excitation of (a) an electronic oscillation of period 1.0 fs, (b) a molecular vibration of period 10 fs, (c) a pendulum of period 1.0 s. Express the results in joules and kilojoules per mole. 【 (a) 6.6 x 10 -19 4.0 x 10 2 (b) 6.6 x 10 -20 40 (c) 6.6 x 10 -34 4.0 x 10 -13 】 1.3 Calculate the energy per photon and the energy per mole of photons for radiation of wavelength (a) 200 nm (ultraviolet), (b) 150 pm (X-ray), (c) 1.00 cm (microwave). 【 (a) 9.93 x 10 -19 J 598kJmol -1 (b) 1.32 x 10 -15 7.97 x 10 -5 (c) 1.99 x 10 -23 0.012 】 1.4 A photon-powered spacecraft of mass 10.0 kg emits radiation of wavelength 225 nm with a power of 1.50 kW entirely in the backward direction. To what speed will it have accelerated after 10.0 y if released into free space? 【 158 ms − 1 】 1.5 Calculate the speed of an electron of wavelength 3.0 cm. 【 2.42 × 10 − 2 ms − 1 】 1.6 The fine-structure constant, α , plays a special role in the structure of matter; its approximate value is 1/137. What is the wavelength of an electron travelling at a speed α c , where c is the speed of light? (Note that the circumference of the first Bohr orbit in the hydrogen atom is 331 pm.) 【 332 pm 】 1.7 Calculate the linear momentum of photons of wavelength 750 nm. What speed does an electron need to travel to have the same linear momentum? 【 8.83 × 10 − 28 kgms − 1 969ms − 1 】 1.8 The energy required for the ionization of a certain atom is 5.12aJ. The absorption of a photon of unknown wavelength ionizes the atom and eject an electron with velocity 345 kms -1 . Calculate the wavelength of the incident radiation. 【 3 . 84 × 10 − 8 m 】 1.9 The Planck distribution gives the energy in the wavelength range dλ at the wavelength λ. Calculate the energy density in the range 650 nm to 655 nm inside a cavity of volume 100 cm 3 when its temperature is (a) 25° C, (b) 3000° C. 【 1.6 × 10 −33 Jm − 3 2.5 × 10 −4 Jm − 3 】 1.10 The wavelength of emission maximum from a small pinhole in an electrically heated container were determined at a series of temperatures, and the results are given below. Deduce a value for Planck’s constant. θ/°C 1000 1500 2000 2500 3000 3500 λ max /nm 2181 1600 1240 1035 878 763