A beam of electrons (m=9.11 x 10 (-31) negative thirty first power has an average speed of 1.3 x 10^8 (eigth power) m*s (-1) s to to the negative first power. What is the wavelength of electrons having this average speed?
Assume your eyes receive a signal crossing of blue light, ^=470nm. The energy of the signal is
2.50 x 10 ^14 (negative 14) J. How many photons reach your eyes?
You have two completely different questions here. Let's address the second first, and then handle the electron problem.
Again, your first problem deals with the photon theory of light. From the photon theory we know two things:
1) In the classical picture, light is a wave (although experiments you are studying right now add to that picture). For any wave the product of wavelength and frequency is the speed of the wave; in this case that speed is the speed of light. So in equation form:
frequency of wave x wavelength of wave = speed of light (3.00 E 8 m/s)
note in my notation 3.00 E8 means 3.00 x 10^8 m/s
The answers are given step-by-step equationally with short explanations.