what's the wavelength ?

Question

A) If the wavelength of an electron is equal to 5.07 x 10^-7 m, how fast is it moving?

B) If the electron has a speed equal to 1.19 x 10^7 m/s, what is its wavelength?

Please show how you solved it, best answer for correct answer. Thanks!

Madhukar · Accepted Answer

A)
Use de Broglie wavelength formula, according to which
wavelength, λ = h/mv, where h = Planck's constant, m = mass of electron and v = its velocity
=> velocity of electron, v 
= h/mλ
= (6.626068 × 10-34) / [(9.10938188 × 10-31) * (5.07 x 10^-7)]
= 
1435 m/s.

https://www.google.co.in/#hl=en&sugexp=frgbld&gs_nf=1&cp=5&gs_id=h&xhr=t&q=Planck's+constant&pf=p&output=search&sclient=psy-ab&oq=Planc&aq=0&aqi=g4&aql=&gs_l=&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.,cf.osb&fp=7a97b5f9bd8de892&biw=1143&bih=661

https://www.google.co.in/#hl=en&sugexp=frgbld&gs_nf=1&pq=planck's%20constant&cp=9&gs_id=36&xhr=t&q=mass+of+electron&pf=p&sclient=psy-ab&oq=mass+of+e&aq=0&aqi=g4&aql=&gs_l=&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.,cf.osb&fp=7a97b5f9bd8de892&biw=1143&bih=661

B)
Use the above formula to find the wavelength. The formula is valid as long as the speed of electron is << speed of light. Otherwise a correction as per Einstein's formula will be needed. 
1.19 x 10^7 m/s = 11900 km/2 << 300000 km/s (speed of light).

Kyle · Answer

Wavelength=speed of light/velocity. So A) 5.07x10^-7=3x10^-8/v.  V=5.92x10^14. B) 3x10^8/1.19x10^7. Wavelength=2.521x10^3. Hope this helps

what's the wavelength ?

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