Respuesta :
Ans: The electron is moving at 0.732% relative to speed of light.
Explanation:
According to the de Broglie relationship:
[tex]\lambda = \frac{h}{mv} [/tex]
So,
[tex]v= \frac{h}{m\lambda} [/tex]
h = Planck's constant = 6.626 * 10^-34 Js
m = mass of electron = 9.11 * 10^-31 kg
λ = wavelength = 3.31 * 10^-10 m
[tex]v= \frac{6.626 * 10^{-34}}{9.11 * 10^{-31}*3.31 * 10^{-10}} [/tex]
[tex]v = 2.197 * 10^6 [/tex]m/s
Since the electron is moving relative to the speed of light, therefore the ratio is(in %):
[tex] \frac{v}{c} *100[/tex]% = [tex] \frac{ 2.197 * 10^6}{3*10^8}*100[/tex]% = 0.732%
Explanation:
According to the de Broglie relationship:
[tex]\lambda = \frac{h}{mv} [/tex]
So,
[tex]v= \frac{h}{m\lambda} [/tex]
h = Planck's constant = 6.626 * 10^-34 Js
m = mass of electron = 9.11 * 10^-31 kg
λ = wavelength = 3.31 * 10^-10 m
[tex]v= \frac{6.626 * 10^{-34}}{9.11 * 10^{-31}*3.31 * 10^{-10}} [/tex]
[tex]v = 2.197 * 10^6 [/tex]m/s
Since the electron is moving relative to the speed of light, therefore the ratio is(in %):
[tex] \frac{v}{c} *100[/tex]% = [tex] \frac{ 2.197 * 10^6}{3*10^8}*100[/tex]% = 0.732%
Since the electron is moving relative to the speed of light, therefore the ratio is 0.732 %
Given :
Mass of an electron, [tex]\rm m_e = 9.11 \times 10^-^3^1\; Kg[/tex]
De-broglie wavelength, [tex]\rm \lambda = 3.31\times 10^-^1^0\; m[/tex]
Speed of light, [tex]\rm c = 3\times 10^8\; m/sec[/tex]
Solution :
We know that de broglie wavelength is given by,
[tex]\rm \lambda = \dfrac{h}{mv}[/tex] ---- (1)
Where,
[tex]\lambda[/tex] is de-broglie wavelength,
m is mass of electron,
h is planck's constant whose value is [tex]6.626\times 10^-^3^4[/tex],
v is velocity.
Now put the values of m, h and [tex]\lambda[/tex] in equation (1) we get,
[tex]\rm v = \dfrac{h}{m \lambda }[/tex]
[tex]\rm v = \dfrac{6.626\times 10^-^3^4}{9.11\times 10^-^3^1 \times 3.31 \times10^-^1^0}[/tex]
[tex]\rm v = 2.197\times 10^6\;m/sec[/tex]
Since the electron is moving relative to the speed of light, therefore the ratio is
[tex]\rm \dfrac{v}{c}\times100 = \dfrac{2.197\times 10^6}{3\times 10^8}\times 100[/tex]
= 0.732 %
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https://brainly.com/question/3479109?referrer=searchResults
