Question on wavelength

[VCEstudentguy]

What wavelength is associated with a beam of neutrons of energy 0.030eV? I tried and I got 4.14*10^-5 which is much too big. The answer is 1.6*10^-10, how do you get there?

[Lasercookie]

I assume you were given the mass of a neutron - just grabbed this off the internet:

We're given this energy:

We know that

So we can figure out


We'll have to convert to Joules,

[VCEstudentguy]

Thank you very much

[VCEstudentguy]

If a potential difference of 40 V was used to accelerate particles, such as a proton or a Helium(+2) ion, then would the Helium have twice the amount of kinetic energy that the proton has?

[Lasercookie]

No.

Let's say for the sake of simplicity that we're accelerating them from rest through a potential difference of 40V. At the end of it, they'll both have absorbed that same amount of energy (and since it was from rest, they'll gain that entire 40 eV).

Their velocities and de Broglie wavelengths will differ though. It won't be by a difference of 1/2 though.

[Aurelian]

No.

Let's say for the sake of simplicity that we're accelerating them from rest through a potential difference of 40V. At the end of it, they'll both have absorbed that same amount of energy (and since it was from rest, they'll gain that entire 40 eV).

Nah, the Helium nucleus would definitely have twice the amount of kinetic energy. The work done on a charged particle accelerated through a potential difference is given by W = qΔV. Since the He nucleus has twice the charge as the proton, it will have twice the amount of work done on it, and hence end up with twice the kinetic energy (if accelerated from rest).

[Lasercookie]

I stand corrected in that case.