What is the Wavelength of Neutrons at Room Temperature?

[scissors]

Hey, this is my first week in Quantum class, going pretty well so far.

My first questoin is:

1.) What is an eV a Unit of...give it in terms of MKS

Well my answer is that it is a unit of energy, and for MKS...

1 Electron*Volt = Joules

1 electron has a charge of 1.602*10^-19 C

1 Volt = 1 J/C

Therefore

1.602*10^-19*1 means that

1 eV = 1.602*10^-19 J

Is this correct reasoning?

My next Question

Neutrons at room Temperature have a kinetic energy of around .02 eV. What is their wavelength?

KE = 0.2 eV

0.2 eV = q*V

p = h/lambda

1 eV = 1.609*10^-19 J

h = 6.626*10^-34 J*s * 1 ev/(1.609*10^-19 J)

Therefore I get Planck's constant in terms of eV

h = 4.136*10^-15 eV*s

But how do I use the 0.2 eV in terms of the p = h/lambda?

Thanks for any assistance!

 

[stunner5000pt]

For the second part i can think of no other way but to get the velocity of the neutrons from the kinetic energy using

$$K = m_{n}c^2(\gamma -1)$$ and then use the De Broglie Hypothesis about wavelength

$$\lambda = \frac{h}{mv}$$

and $$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$

 

[Dr Transport]

$$E = \frac{ \hbar c} {\lambda}$$

 

[scissors]

Thanks! But I'm looking at my notes, and it says that the equation applies only to massless particles?

 

[Dr Transport]

$$E^{2} = p^{2}c^{2} + m_{0} ^{2} c^{4}$$ is the expression for particles with mass.

 

[dextercioby]

1.NEUTRONS HAVE REST MASS.

2.U don't need the relativistic formula.
$$\lambda=\frac{h}{p}=\frac{h}{\sqrt{2mE}}$$

Daniel.