Experts kindly solve it in detail - Physics - Dual Nature Of Radiation And Matter

Question

Experts kindly solve it in detail

Vipra Mishra · Accepted Answer

Dear Student
Let's think of the electron as a particle It has a certain mass, m,
and a velocity, v The momentum of the particle is the mass times
the velocity, p=mv The energy of the electron is its kinetic
energy
E = ½ m v2 = p2/2m

Now let's think of the electron as a de Broglie particle wave In a
box of length L, the allowed wavelengths are given by our result
for the standing waves formed by a string of length L
λn = 2L/n n = 1,2,3

Only certain allowed wavelengths are possible

If we combine this result with deBroglie's relation, we find that
only certain allowed momenta are possible
pn = h/λn = nh/2L n = 1,2,3

So correct option is 1

Regards

Experts kindly solve it in detail.