## 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

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.

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1. We can solve the problem by using De Broglie’s relationship:
[tex]p= mv= frac{h}{lambda} [/tex]
where
p is the momentum of the particle
m is the the mass
v is the velocity
h is the Planck constant
[tex]lambda[/tex] is the wavelength of the particle

By re-arranging the equation, we get
[tex]lambda = frac{h}{mv} [/tex]
and by using the data about the proton mass and speed, we find its wavelength:
[tex]lambda= frac{6.6 cdot 10^{-34} Js}{(1.66 cdot 10^{-27} kg)(5.0 cdot 10^6 m/s)}=7.95 cdot 10^{-14} m [/tex]

2. The wavelength is indirectly proportional to the mass and velocity of the particle. The wavelength of the given proton is [tex]7.95 times 10^{-14}[/tex].

## From de Broglie’s relationship:

[tex]lambda = dfrac h{mv}[/tex]

Where,

[tex]m[/tex] – mass = [tex] 1.66 times 10^{-27}rm kg [/tex]

[tex]v[/tex] – velocity = [tex]5.0 times 10^6 rm m/s[/tex]

[tex]h[/tex] – Planck constant = [tex] {6.6times 10^{-34}}rm Js[/tex]

[tex]lambda [/tex] – wavelength of the particle = ?

Put the values in the formula,

[tex]lambda = dfrac {6.6times 10^{-34}}{(1.66times 10^{-27})(5.0 times 10^6)}nlambda = 7.95 times 10^{-14}[/tex]

Therefore, the wavelength of the given proton is [tex]7.95 times 10^{-14}[/tex].