problem 36 and 37 The 12C160 molecule has an equilibrium bond distance of 112.8

Question

problem 36 and 37

The 12C160 molecule has an equilibrium bond distance of 112.8 pm. Calculate (a) the reduced mass and (b) the moment of inertia, (c) Calculate the wavelength of the photon emitted when the molecule makes the transition from l = 1 to l = 0 using equation 9.144 for the energy levels. (a) The distribution of wavelengths from a certain star peaks in the visible at lambda = 600 nm. Assuming that the distribution obeys the Planck distribution law, use Wien's displacement law to estimate the temperature of the star, (b) A metal bar is heated to red heat so that its radiation peaks at lambda = 800 nm. Estimate the temperature of the bar. (a) Derive the value of the constant in the Wien displacement law (equation 9.186) in terms of h, c, and k. (b) If, from experiment, the values of h and c were measured to

Explanation / Answer

a) reduced mass = m1m2/(m1+m2 ) = (12x16)/(12+16) = 6.857 amu , = 6.857 x1.66 x10^ -27 = 1.138 x10^ -26 kg b) I = mr^2 = 1.138 x10^ -26 x (112.8 x10^ -12)^2 = 1.448 x10^ -46 kgm^2 , 37) a) lamda x T = 0.002897 , is formula , lamda = 600 nm = 600 x10^ -9 m , T = 0.002897 /(600 x10^ -9) = 4828.33 K is temp of star , b) T = 0.002897/( 800 x 10^ -9) = 3621.25 K is temp of rod ,

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