Question

One way to probe the nucleus is to bombard a sample with high-energy electrons. To learn about the nuclear structures in a sample, the de Broglie wavelengths of these electrons would need to be a little smaller than a nuclear radius. Estimate the energy of such electrons. Give your answer in electron-volts. (Assume that the wavelength used is about 9.0 fm.) eV

Answer 1

E = 1.38 x 10⁸ eV = 138 MeV

Step-by-step explanation:

The energy associated with the given wavelength can be found from the following formula:

`E = (hc)/(\lambda)`

where,

E = Energy of electron = ?

h = Plank's Constant = 6.625 x 10⁻³⁴ J.s

c = Speed of Light = 3 x 10⁸ m/s

λ = wavelength = 9 fm = 9 x 10⁻¹⁵ m

Therefore,

`E = ((6.625\ x\ 10^(-34)\ J.s)(3\ x\ 10^8\ m/s))/(9\ x\ 10^(-15)\ m)\\\\E = (2.21\ x\ 10^(-11)\ J)((1\ eV)/(1.6\ x\ 10^(-19)\ J))`

E = 1.38 x 10⁸ eV = 138 MeV