Question

To resolve an object in an electron microscope, the wavelength of the electrons must be close in the diameter of the object. What kinetic energy must the electrons have in order to resolve a protein molecule that is 9.00nm in diameter? Take the mass of an electron to be 9.11 X10 ^-31

How many photons are produced in a laser pulse of 0.435 J at 449nm?

Answer 1

1st Question:

From De-Broglie wavelength equation

let us use the expression wave length L = h/mv

We know the kinetic energy E = 1/2 mv2, v2 = 2E/m

if substituted in above equation L2 = h2/m.2E

Hence E =( h^2 / L^2 )(1/2m)

Here E is the required kinetic energy in joule
Now we have h = 6.626 x 10^-34 J s, L = 9 x 10^-9 m,

mass of an electron m = 9.11 x 10 ^-31 , hence

       =     2.97 x 10^-21 J

2nd Question:

E = hc / L

E = energy per photon...
h = plancks constant = 6.626x10^-34 J s
c = speed of light = 3.00x10^8 m/s
L = wavelength = 449 nm = 449x10^-9 m

Energy per photon (E )    = 4.43 x10^-19 J

For 0.435 J,

photons produced =   0.435 J x (1 photon / 4.43 x10^-19 J )

                               = 9.8 x 10^17 Photons