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The de Broglie wavelength 
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#1
Mar208, 05:29 PM

P: 18

The mass of an electron is 9.11*10^31 kg. If the de Broglie wavelength for an electron in an hydrogen atom is 3.31*10^10 m, how fast is the electron moving relative to the speed of light? The speed of light is 3.00*10^8 m/s.
here's what I did: i solved for velocity=6.626*10^34J/(9.11*10^31kg)(3.31*10^10) v=2.1974*10^74 and i tried to gain the percent by dividing the speed of light by velocity. where did i go wrong? 


#2
Mar208, 05:46 PM

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P: 5,196

Your calculation is wrong. Don't just blindly do calculations. Think...does the number your calculator has spewed out actually make any sense? When it's something ridiculous like 10^74 m/s, the answer is emphatically NO. Kind of slow for a particle, don't you think?
I get v = (0.00732)c 


#3
Mar208, 05:53 PM

P: 173

how did u calculate.... watch the exponents first...... the magnitude is 10^7 m/s... [tex]\frac{6}{9\times3}\times\frac{10^{34}}{10^{31}\times10^{10}}\approx\frac{2}{9}10^7 m/s[/tex] this suggest us that it is better to treat the electron relativistically if we want to penetrate deep in its properties... regards marco 


#4
Mar208, 06:05 PM

P: 173

The de Broglie wavelength
thanx Dirac :)



#5
Mar208, 08:40 PM

P: 18

so hows do i get the percentage here's what i'm doing: 3.00*10^8 m/s /100 = 0.00732/x. x=2.4*10^8, but i know this isn't right so, what shall i do?



#6
Mar208, 11:49 PM

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P: 5,196

I'm not sure what percentage you are talking about, since it's not mentioned in the original post.
For the velocity of the particle, I get: [tex] v = 2.197 \times 10^6 \ \ \ \frac{\textrm{m}}{\textrm{s}} [/tex] The question asks how fast the particle is moving relative to the speed of light. Well, their ratio is [tex] \frac{v}{c} = \frac{2.197 \times 10^6 \ \ \ \textrm{m/s}}{3.00 \times 10^8 \ \ \ \textrm{m/s}} = 0.00732 [/tex] So, expressed in units of the speed of light, the velocity is [tex] v = 0.00732c [/tex] The particle is moving at 0.00732 times the speed of light. Obviously, as a percentage, that's 0.732%. So I guess if you wanted to, you could say that the particle is moving at 0.732% of the speed of light. It's a completely equivalent statement though. It doesn't add any extra meaning. 


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