An electron microscope employs a beam of electrons to obtain an image of an object. What energy must be imparted to each electron of the beam to obtain a wavelength of 15.2 pm? Obtain the energy in electron volts (eV) (1 eV = 1.602 10-19 J).

Question

An electron microscope employs a beam of electrons to obtain an image of an object. What energy must be imparted to each electron of the beam to obtain a wavelength of 15.2 pm? Obtain the energy in electron volts (eV) (1 eV = 1.602  10-19 J).

DrBob222 · Accepted Answer

E = hc/wavelength Plug in the wavelength, calculate E (in Joules) and convert to eV.

Robert Simazuo · Answer

firstly find the speed of the electron by using the formula wavelength =Planck's constant / mass * velocity( speed) as the speed of light does not apply in this case as electrons are slower and not part of EMR. make speed the subject of the formula. after finding speed use the equation E=hv/ wavelength. after obtaining the energy in joules convert the joules to eV as required by the question.
mass of an electron is equal to 9.11 *10^-31 kg
planck's constant =6.626 *10^-34
wavelength given is 10.0 pm =1*10*-11 m
final answer should be 3eV

Bot · Answer

To find the speed of the electron, we can rearrange the formula:

wavelength = Planck's constant / (mass * velocity)

Rearranging for velocity:

velocity = Planck's constant / (mass * wavelength)

Plugging in the values:

velocity = (6.626 * 10^-34) / (9.11 * 10^-31 * 15.2 * 10^-12)
= 45655.8 m/s

Now we can use the equation E = (Planck's constant * velocity) / wavelength to calculate the energy:

E = (6.626 * 10^-34 * 45655.8) / (15.2 * 10^-12)
= 1.988 * 10^-25 J

To convert this to electron volts (eV), we can use the conversion factor:

1 eV = 1.602 * 10^-19 J

Converting:

Energy in eV = (1.988 * 10^-25) / (1.602 * 10^-19)
= 1.24 * 10^-6 eV

So the energy imparted to each electron of the beam is approximately 1.24 * 10^-6 eV.