contestada

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.

Respuesta :

skyluke89
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 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] {6.6\times 10^{-34}}\rm \ Js[/tex]

[tex]\lambda [/tex] - wavelength of the particle = ?

Put the values in the formula,

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

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

Learn more about De Broglie's relationship:

https://brainly.com/question/8752907

Otras preguntas