The seeing ability, or resolution, of radiation is determined by its wavelength. If size of an atom is
of the order of 0.1 nm, how fast must an electron travel to have a wavelength small enough to “see” an
atom?
The electron wavelength (h/mv)should be comparable to the atom size, or less.
h is Planck's constant. m is the electron mass.
Use the relationship above to get the required minimum electron momentum.
Divide that by the electrobn mass for the thew requkired electron speed.
To determine how fast an electron must travel to have a wavelength small enough to "see" an atom, we can use the de Broglie wavelength equation:
λ = h / p
Where:
λ is the wavelength of the electron
h is the Planck's constant (6.626 x 10^-34 J·s)
p is the momentum of the electron
The momentum of an electron can be calculated as:
p = m * v
Where:
m is the mass of the electron (9.109 x 10^-31 kg)
v is the velocity of the electron
Since we are trying to find the minimum velocity of the electron in order to have a small enough wavelength, we can use the following equation:
λ = h / (m * v)
Rearranging the equation, we can solve for v:
v = h / (m * λ)
Now let's substitute the given values into the equation:
λ = 0.1 nm = 0.1 x 10^-9 m
Plugging in the values:
v = (6.626 x 10^-34 J·s) / (9.109 x 10^-31 kg) * (0.1 x 10^-9 m)
Simplifying the calculation:
v = 7.27 x 10^6 m/s
Therefore, the electron must travel at least 7.27 x 10^6 meters per second to have a wavelength small enough to "see" an atom.