An electron of a velocity 'x' is found to have a certain wavelength. T...
Explanation:
De Broglie wavelength:
De Broglie wavelength is the wavelength associated with the motion of a particle. It is given by the formula:
λ = h/p
Where λ is the wavelength, h is the Planck's constant, and p is the momentum of the particle.
Relation between velocity and momentum:
The momentum of a particle is related to its velocity by the formula:
p = mv
Where p is the momentum, m is the mass of the particle, and v is the velocity of the particle.
Calculating the velocity of the neutron:
We are given the velocity of the electron and the wavelength associated with its motion. We need to find the velocity of the neutron that would have half the de Broglie wavelength of the electron.
Let the velocity of the neutron be v_n. Then, we can write:
λ_n/2 = h/p_n
Where λ_n/2 is half the de Broglie wavelength of the electron, and p_n is the momentum of the neutron.
We can also write:
p_n = mv_n
Substituting the second equation into the first equation, we get:
λ_n/2 = h/mv_n
Simplifying this equation, we get:
v_n = h/(mλ_n/2)
We know that the de Broglie wavelength of the electron is given by:
λ_e = h/mev_e
where me is the mass of the electron.
Substituting this equation into the previous expression for v_n, we get:
v_n = h/(mλ_e/4)
Simplifying this equation, we get:
v_n = 4hv_e/(mλ_e)
Now, we can substitute the given value of v_e and solve for v_n:
v_n = 4hv_e/(mλ_e) = 4h(x)/(meλ_e) = (4/1840)x
Therefore, the velocity of the neutron that would have half the de Broglie wavelength of the electron is x/920, which is option (B).
Answer: B) x/920.