Recall the Bohr model of the hydrogen atom (1910), in which the electron is assumed to move around a circle with radius r. The model is based on two equations: (1) Newton's 2nd law for circular motion, and (2) Bohr's hypothesis of quantized angular momentum. (A) For quantum number n = 2, what is the electron speed? (B) Again for n = 2, what is the electron energy in electron-volts?

In an electron microscope, we wish to study particles of diameter about 0.10 μm (about 1000 times the size of a single atom). (a) What should be the de Broglie wave- length of the electrons? (b) Through what potential dif- ference should the electrons be accelerated to have that de Broglie wavelength?

Suppose two electrons in an atom have quantum numbers n= 2 and L=1 . (a) How many states are possible for those two electrons? (Keep in mind that the electrons are indistinguishable.) (b) If the Pauli exclusion principle did not apply to the electrons, how many states would be possible?

Consider a Bohr model of doubly ionized lithium (Z = 3) . (a) Write an expression for the energy levels of the sole remaining electron. (b) Find the energy corresponding to n = 4 . (c) Find the energy corresponding to n2. (d) Calculate the energy of the photon emitted when the electron n = 2 transits from the fourth energy level to the second energy level. Express the answer both in electron volts and in joules. (e) Find the frequency and wavelength of the emitted photon () In what part of the spectrum is the emitted light? (h=6.63*10^ -34 .5 , c=3.00*10^ 8 m/s,nm=10^ -9 m) , 1 eV=1.66*10^ .19 J)

What is the wavelength of a photon emitted when an electron jumps from the n=3 to the n=2 energy levels of a lithium atom (Z=3)? Express your answer in nanometers and keep three significant digits.