The resolving power of a microscope is proportional to the wavelength used. A resolution of 1.0 10-11 m (0.010 nm) would be required in order to "see" an atom. (a) If electrons were used (electron microscope), what minimum kinetic energy would be required for the electrons

K = 13448.64eV

Explanation:

(a) In order to calculate the kinetic energy of the electrons, to "see" the atom, you take into account that the wavelength of the electrons must be of the order of the resolution required (0.010nm).

Then, you first calculate, by using the Broglies' relation, the momentum of the electron associated to a wavelength of 0.010nm:

      (1)

p: momentum of the electron

h: Planck's constant = 6.626*10^-34 Js

λ: wavelength = 0.010nm

You replace the values of the parameters in the equation (1):

With this values of the momentum of the electron you can calculate the kinetic energy of the electron by using the following formula:

   (2)

m: mass of the electron = 9.1*10^-31 kg

In electron volts you obtain:

The kinetic energy required for the electrons must be, at least, of 13448.64 eV

firearm identification is the process of analyzing the bullets and cartridge cases left at a crime scene to determine if they came from a particular firearm. marks on the bullets and cartridges may be common to every firearm of that type. these are called class characteristics.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .