Help me understand the de Broglie equation??

The de Broglie equation relates wavelength of a mass-ive particle to its momentum:

#lambda = h/p = h/(mv)#

where:

• #lambda# is wavelength in #"m"#.
• #h = 6.626 xx 10^(-34) "J"cdot"s"# is Planck's constant.
• #p# is linear momentum in #"kg"cdot"m/s"#.
• #m# is mass in #"kg"#. That is, the particle MUST have a nonrelativistic mass.
• #v# is speed in #"m/s"#.

If you couldn't tell, this CANNOT work on photons. (Why not?)

Here are two examples:

1. Calculate the momentum of an electron with de Broglie wavelength #5.0 xx 10^(-34) "m"#.

#p = h/lambda#

#= (6.626 xx 10^(-34) "kg"cdot"m"^cancel(2)"/s")/(5.0 xx 10^(-34) cancel"m")#

#= "1.33 kg"cdot"m/s"#

This is an ordinary, 'classical' value of the momentum, which means that everyday particles (e.g. basketballs, socks, etc) must have extremely small wavelengths (which they do).

2. Which wavelength corresponds to the photon with the fastest speed in vacuum?

#a)# #"500 nm"#
#b)# #"500 pm"#
#c)# #"500 cm"#
#d)# All of the above

I'll let you tell me which of these answers you think is correct (#a,b,c,d#).