De Broglie wavelength: maximum mass allowed?

[rainingspiders]

I thought I was doing this right until I saw the answer in the back of the book.... is it a typo, or am I doing something wrong?

 

Question: Assuming that the smallest measurable wavelength in an experiment is 0.10 femtometers, what is the maximum mass of an object traveling at 100 m/s for which the de Broglie wavelength is observable?

 

My method:

 

equation:

wavelength = (plank's constant) / (momentum)

wavelength = (plank's constant) / (mv)

0.10 * 10^-15 m = (6.626 x 10^-34) / (m * (100))

 

Solving from m...

I got 6.6 * 10^-20 kg?

 

But in the back of the book, it says 6.6 * 10^-29 kg?

 

Did I do something wrong? Or did someone typed 9 instead of 0?

[Endy0816]

Yeah, I received the same result using (6.626×10^-34) /[(100)×(0.1×10^-15)].

[Sensei]

Isn't momentum relativistic?

 

[math]p=m_0*v*\gamma[/math]

 

[math]\lambda=\frac{h}{p}[/math]

 

[math]\lambda=\frac{h}{m_0*v*\gamma}[/math]

 

Although, [math]100\frac{m}{s}[/math] isn't relativistic velocity.

 

Edited November 11, 2014 by Sensei

[rainingspiders]

@organism: what does "relativistic" mean?

 

I'm not sure... the equation my textbook gave me says if the speed is not close to the speed of light, the momentum is mv?

So I'm guessing it's a typo then?

[swansont]

I also vote typo. I get the same answer as both of you.

[ajb]

Just a general comment on things like this. In my experience students often make mistakes with the exponents, sometimes with the minus, sometimes they get the pre-factors like micro confused and sometimes they just go wrong with how exponents work. What I would usually suggest is that the student think about what that value means. Does it sound physically reasonable? Sometimes this can show you have an error.

 

However in this case it won't work. Either mass is physically reasonable for a particle.

 

The tobacco mosaic virus has mass 10^-20 kg

The muon has mass 10^-28 kg

The quarks have mass 10^-30 kg

The electron has mass 10^-31 kg

[Sensei]

The electron has mass 10^-31 kg

 

Rest mass of electron is more likely 9.11*10^-31 kg. That's nearly 10^-30 kg, not 10^-31 kg.

That's why it's good to remember exact values..

[ajb]

 

Rest mass of electron is more likely 9.11*10^-31 kg. That's nearly 10^-30 kg, not 10^-31 kg.

That's why it's good to remember exact values..

 

 

Sure, but for checking orders of magnitude for many questions this is not so important. But you are right, it is closer to 10^-30 kg.

[rainingspiders]

That's good to hear. Thanks for all your help!