# Chemistry Question

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• April 23rd 2010, 11:25 PM
A Beautiful Mind
Chemistry Question
Gah.

Question: In particle accelerators, protons can be accelerated to speeds near that of light. Estimate the wavelength in nm of such a proton moving at $2.40 * 10^8$ m/s. (mass of proton = $1.673 * 10^{-27}$kg)

Here's the work I've done:

It says to use deBrogile's equation:

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

h stands for Planck's constant = $6.63*10^{-34} {kgm^2}{s}$
m for the mass = $1.673*10^{-27}$ kg
u for the speed = $2.40*10^8$ m/s

Plugging in...

$\frac {6.63*10^{-34} kgm^2}{(2.40*10^8 m/s)(1.673*10^{-27}kg})$

= $1.65*10^{-15}$ m

Conversion factors for nm:

$\frac{1m}{1*10^{-9}nm} = \frac{1*10^{-9}nm}{1m}$

And then I get wrong answers all over the place. I keep constantly getting new wrong answers and even on Yahoo they're giving me wrong answers. Totally don't know what I'm doing wrong.
• April 24th 2010, 12:36 AM
mathaddict
Quote:

Originally Posted by A Beautiful Mind
Gah.

Question: In particle accelerators, protons can be accelerated to speeds near that of light. Estimate the wavelength in nm of such a proton moving at $2.40 * 10^8$ m/s. (mass of proton = $1.673 * 10^{-27}$kg)

Here's the work I've done:

It says to use deBrogile's equation:

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

h stands for Planck's constant = $6.63*10^{-34} {kgm^2}{s}$
m for the mass = $1.673*10^{-27}$ kg
u for the speed = $2.40*10^8$ m/s

Plugging in...

$\frac {6.63*10^{-34} kgm^2}{(2.40*10^8 m/s)(1.673*10^{-27}kg})$

= $1.65*10^{-15}$ m (from here , just divide by 10^(-9))

Conversion factors for nm:

$\frac{1m}{1*10^{-9}nm} = \frac{1*10^{-9}nm}{1m}$

And then I get wrong answers all over the place. I keep constantly getting new wrong answers and even on Yahoo they're giving me wrong answers. Totally don't know what I'm doing wrong.

.
• April 24th 2010, 12:39 AM
ADARSH
Quote:

Originally Posted by A Beautiful Mind
Gah.

Question: In particle accelerators, protons can be accelerated to speeds near that of light. Estimate the wavelength in nm of such a proton moving at $2.40 * 10^8$ m/s. (mass of proton = $1.673 * 10^{-27}$kg)

Here's the work I've done:

It says to use deBrogile's equation:

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

h stands for Planck's constant = $6.63*10^{-34} {kgm^2}{s}$
m for the mass = $1.673*10^{-27}$ kg
u for the speed = $2.40*10^8$ m/s

Plugging in...

$\frac {6.63*10^{-34} kgm^2}{(2.40*10^8 m/s)(1.673*10^{-27}kg})$

= $1.65*10^{-15}$ m

Conversion factors for nm:

$\frac{1m}{1*10^{-9}nm} = \frac{1*10^{-9}nm}{1m}$

And then I get wrong answers all over the place. I keep constantly getting new wrong answers and even on Yahoo they're giving me wrong answers. Totally don't know what I'm doing wrong.

Dont you think the mass would change if speed nears speed of light

relation
:

$m'=\frac{m}{\sqrt{1-(\frac{v}{c})^2}}$

I guess its related to the first line of your question

-Adarsh
• April 24th 2010, 12:51 AM
A Beautiful Mind
Quote:

Originally Posted by mathaddict
.

I tried that before and just now. It's not the right answer.
• April 24th 2010, 01:31 AM
ADARSH
Is your answer

$=0.99 \cdot 10^{-6}nm$ ?

if yes than its from the relative mass relation I had mentioned.

Mass in special relativity - Wikipedia, the free encyclopedia

We have to take the realtive mass/momentum in consideration for your question,since the speed is comparable to speed of light.