Compare the wavelengths of an electron (mass = 9.11 × 10−31 kg) and a proton (mass = 1.67 × 10−27 kg), each having (a) a speed of 6.55 × 106 m/s and (b) a kinetic energy of 7.89 × 10−15 J. Enter your answers in scientific notation.

Part A:

The proton has a smaller wavelength than the electron.  

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Part B:

The proton has a smaller wavelength than the electron.

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Explanation:

The wavelength of each particle can be determined by means of the De Broglie equation.

(1)

Where h is the Planck's constant and p is the momentum.

(2)

Part A

Case for the electron:

But

Case for the proton:

Hence, the proton has a smaller wavelength than the electron.  

Part B

For part b, the wavelength of the electron and proton for that energy will be determined.

First, it is necessary to find the velocity associated to that kinetic energy:

 (3)

Case for the electron:

but

Then, equation 2 can be used:

Case for the proton :

But

Then, equation 2 can be used:

Hence, the proton has a smaller wavelength than the electron.

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explanation: