Question

a proton is in a box of width L. what must the width of the box be for the ground level energy to be 5.0 MeV, a typical value for the energy with which the particles in a nucleus are bound

Answer 1

Answer:

Width of a box, $l=6.41\times 10^{-15}\ m$

Explanation:

The ground level energy of a proton in a box is, E = 5 MeV

$E =5\times 10^6\ eV\\\\=5\times 10^6\times 1.6\times 10^{-19}\\\\=8\times 10^{-13}\ J$

Energy in a box is given by :

$E=\dfrac{n^2h^2}{8ml^2}$

For ground state, n = 1

m is mass of proton

h is Planck's constant

l is width of the box

$l^2=\dfrac{n^2h^2}{8mE}\\\\l^2=\dfrac{1^2\times (6.63\times 10^{-34})^2}{8\times 1.67\times 10^{-27}\times 8\times 10^{-13}}\\\\l=\sqrt{\dfrac{1^{2}\times(6.63\times10^{-34})^{2}}{8\times1.67\times10^{-27}\times8\times10^{-13}}}\\\\l=6.41\times 10^{-15}\ m$

So, the width of the bx is $6.41\times 10^{-15}\ m$.