## 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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2022-05-14T05:56:17+00:00
2022-05-14T05:56:17+00:00 2 Answers
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## Answers ( 2 )

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]

The

wavelengthis indirectly proportional to themassandvelocityof the particle. Thewavelengthof the givenprotonis [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] –

Planckconstant = [tex] {6.6times 10^{-34}}rm Js[/tex][tex]lambda [/tex] –

wavelengthof the particle = ?Put the

valuesin 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

wavelengthof the givenprotonis [tex]7.95 times 10^{-14}[/tex].Learn more about

De Broglie’s relationship:https://brainly.com/question/8752907