Respuesta :

Answer:

0.449  10^(-8)  meters

[tex]0.449 * 10^{-8}[/tex] meters

Explanation:

Use the deBroglie equation for the wavelength (lambda):

[tex]lambda = \frac{h}{m*v}[/tex]

where h stands for the Plank constant: [tex]6.6261 * 10^{-34} J[/tex]

m stands for the mass of the electron: [tex]9.109 * 10^{-31} kg[/tex]

and v is the given velocity: [tex]v = 1.62 *  10^5 \frac{m}{s}[/tex]

Evaluating lambda for these values:

[tex]lambda = \frac{h}{m*v}= \frac{6.6261 * 10^{-34} }{9.109 * 10^{-31} * 1.62 * 10^{5}} = 0.449* 10^{-8} m[/tex]

Answer : The wavelength of an electron is, [tex]4.39\times 10^{-9}m[/tex]

Explanation :

According to de-Broglie, the expression for wavelength is,

[tex]\lambda=\frac{h}{p}[/tex]

and,

[tex]p=mv[/tex]

where,  

p = momentum, m = mass, v = velocity

So, the formula will be:

[tex]\lambda=\frac{h}{mv}[/tex]

where,

h = Planck's constant = [tex]6.626\times 10^{-34}Js[/tex]

[tex]\lambda[/tex] = wavelength  = ?

m = mass  of electron = [tex]9.31\times 10^{-31}kg[/tex]

v = velocity = [tex]1.62\times 10^5m/s[/tex]

Now we have to calculate the wavelength.

Now put all the given values in the above formula, we get:

[tex]\lambda=\frac{h}{mv}[/tex]

[tex]\lambda=\frac{6.626\times 10^{-34}Js}{(9.31\times 10^{-31}kg)\times (1.62\times 10^5m/s)}[/tex]

[tex]\lambda=4.39\times 10^{-9}m[/tex]

Therefore, the wavelength of an electron is, [tex]4.39\times 10^{-9}m[/tex]

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