A particle is placed inside a box. Its energy was determined to be 36•Eg. This partice exists in a non-stationary energy state. True O False Question 4 A particle is placed inside a box. Its energy was determined to be 17•Eg. This partice exists in a non-stationary energy state. O True False

The energies of macroscopic objects, as well as those of microscopic objects, are quantized, but the effects of the quantization are not seen because the difference in energy between adjacent states is so small. Apply Bohr’s quantization of angular momentum to the revolution of Earth (mass6.01024kg) , which moves with a speed of 3.0104ms1 in a circular orbit (radius1.51011m) about the sun. The sun can be treated as fixed. Calculate the value of the quantum number n for the present state of the Earthsun system. What would be the effect of an increase in n by 1?

A beam of light can be thought of as consisting of a stream of light particles called .

(a) Using Equation 4.36, make a graph of the n=3 wave function and the square of this wave function for a particle in a box with the edges at x=0 and x=7 . Estimate the probability of finding the particle between x1=3 and x2=4 . You may either do an integral or find the area under the curve by counting the number of rectangular boxes (roughly estimating the fractional boxes), and then multiply by the area of each box, watching your units. Show your calculation with units for credit. (b) Verify that the n=3 wave function in (a) is an allowed quantum state (sometimes called an eigenfunction) of by substituting it for in the left side of the equation =E immediately following Eq. 4.32. Calculate the derivatives to see if your result E is a constant multiplied by the original n=3 wavefunction. What does the constant you get tell you about the energy of thiseigenstate? Is it in agreement with the energy for the n=3 level you would calculate from Equation 4.37?