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]
