What is the wavelength of a proton with a speed of 5.00 E6 m/s?

Question

Using Planck’s constant as h = 6.63 E-34 J*s, what is the wavelength of a proton with a speed of 5.00 E6 m/s? The mass of a proton is 1.66 E-27 kg.

Answer 1

7

Answer 2

The de Broglie wavelength w of a particle is found by dividing Planck's

constant by the particle's momentum; that is w = h/p or w = h/mv.

We are given m as 1.66 * 10**-27 kg. and the speed as 5 * 10**6 m/s

(5 million meters per second) then the momentum p equals mv, or

p = mv = 8.3 * 10**-21 kg-m/sec.

If we divide Planck's constant, 6.627 * 10**-34 J-sec by the momentum

we get 0.7984 * 10**-13meter, or 79.84 femtometers.

We can say the wavelength is 79.84 fm. or 7.984 * 10**-14 meter

which is very short!