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.

Remember to identify your data, show your work, and report the answer using the correct number of significant digits and units.

Answer 1

7.00 x 10-14 meters

Step-by-step explanation:

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Answer 2

De Broglie's identity gives the relationship between the momentum and the wavelength of a particle:

`p=mv= (h)/(\lambda)`
where
p is the particle momentum
m is its mass
v its velocity
h is the Planck constant

`\lambda` is the wavelength

By re-arranging the equation, we get

`\lambda= (h)/(mv)`
and by using the data about the proton, given in the text, we can find the proton's wavelength:

`\lambda= (h)/(mv) = (6.63 \cdot 10^(-34) Js)/((1.66 \cdot 10^(-27) kg)(5.00 \cdot 10^6 m/s)) =7.99 \cdot 10^(-14) m`