How Do You Calculate Neutron Wavelength?

[jjson775]

Homework Statement

Show that the wavelength of a neutron is (2.86x10-11/√K)m where K is the kinetic energy in electron volts.

Relevant Equations

λ=h/mv

λ^2=h^2/m^2v^2
=h^2/2/(m^2v^2/2)
=h^2/2/(Km)
=h^2/2Km

 

[BvU]

Is there a question here ?

As an urgent hint: use brackets where necessary !

 

[jjson775]

Is there a question here ?

As an urgent hint: use brackets where necessary !

There are 2 brackets missing in the homework statement. They look OK to me in the attempted solution. I can't get to the answer (λ in terms of K and m) from my last line. m should be in the numerator.

 

[kuruman]

m should be in the numerator.

You mean denominator.

 

[jjson775]

You mean denominator.

 

[jjson775]

No, numerator is correct. Actually, when I looked again at the homework statement, the brackets are OK.

 

[kuruman]

No, numerator is correct. Actually, when I looked again at the homework statement, the brackets are OK.

The mass in the numerator is not correct.

Spoiler

$K=\dfrac{p^2}{2m}~\Rightarrow~p=\sqrt{2mK}$.

$\lambda=\dfrac{h}{p}=\dfrac{h}{\sqrt{2mK}}.$

 

[jjson775]

m is shown in the numerator in the textbook. See attached file.

 

[kuruman]

I saw the attached file and the mass is in the denominator. You are just confused about which is which.
From https://www.freemathhelp.com/numerator-denominator.html

 

[jjson775]

See Problem 3

 

[kuruman]

That "m" stands for "meters" not "mass". In other words, if you enter a number for the kinetic energy in electron volts, take the square root and divide the result into 2.86 x 10^-11, the result will be in meters. I dislike mixed unit formulas of this kind exactly because of the confusion they sow as we have seen in this case.

Do you know how to proceed now?

 

[vela]

See Problem 3

The variable $m$ is usually typeset in an italic font whereas the unit m is not.

 

[kuruman]

The variable $m$ is usually typeset in an italic font whereas the unit m is not.

Unfortunately the textbook page where the formula appears was posted a few replies after the confusion had already set in.

 

[jjson775]

I am actually past this point in the book and knew I was hung up on something silly with this problem, which was the case. I mixed up the m for mass with meters. A mental block. I am a retired engineer, 78 years old, seeing modern physics for the first time. Past special relativity and now in QM. Thanks.

 

[kuruman]

I am actually past this point in the book and knew I was hung up on something silly with this problem, which was the case. I mixed up the m for mass with meters. A mental block. I am a retired engineer, 78 years old, seeing modern physics for the first time. Past special relativity and now in QM. Thanks.

Good luck with your endeavor. We are here to help.