An electron and a neutron each have a kinetic energy of 10eV. What are their deB

Question

An electron and a neutron each have a kinetic energy of 10eV. What are their deBrolgie wavelengths? {The reason for this question is that we were using a step (i.e. sudden) change in potential in several problems. This is not too bad if the actual potential changes in a fraction of the deBroglie wavelength.} PLEASE EXPLAIN WITH FULL DETAIL TO BE SELECTED AS BEST ANSWER.

An electron and a neutron each have a kinetic energy of 10eV. What are their deBrolgie wavelengths? {The reason for this question is that we were using a step (i.e. sudden) change in potential in several problems. This is not too bad if the actual potential changes in a fraction of the deBroglie wavelength.

Explanation / Answer

Are you familiar with the De Broglie relationship, or are you studying in advance? ;-)

You need to use the final 2 equations you stated.

From E=1/2 * m * v^2

2E = m v^2
2Em = (m v)^2
2Em = p^2 p=momentum
p = (2Em) ^ 0.5
h/lambda = (2Em) ^0.5

for e- wavelength =h/(2Em)^0.5 =6.626*10^-34/(2*10*1.6*10^-19*9.1*10^-31)^0.5 =3.88*10^-10 m

for neutron substitute m=1.675*10^-27 kg

we get wavelength =9*10^-12 m

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