Respuesta :
Answer:
DeBroglie wavelength is [tex]2.42\times 10^{-10}\ m[/tex]
Frequency is [tex]1.24\times 10^{16}\ Hz[/tex]
Explanation:
Mass of electron = 9.10938356 × 10⁻³¹ kg
Planck's constant = h = 6.626 × 10⁻³⁴ m²kg/s
Speed of light = c = 3×10⁸ m/s
[tex]\lambda=\frac{h}{p}=\frac{h}{mv}\\\Rightarrow \lambda=\frac{6.626\times 10^{-34}}{9.10938356\times 10^{-31}\times \frac{3\times 10^8}{100}}\\\Rightarrow \lambda=2.42\times 10^{-10}\ m[/tex]
DeBroglie wavelength is [tex]2.42\times 10^{-10}\ m[/tex]
[tex]v=f\lambda\\\Rightarrow f=\frac{v}{\lambda}\\\Rightarrow \frac{\frac{3\times 10^8}{100}}{2.42\times 10^{-10}}\\\Rightarrow f=1.24\times 10^{16}\ Hz[/tex]
Frequency is [tex]1.24\times 10^{16}\ Hz[/tex]
Answer:
[tex]\lambda=2.42\times 10^{-10}\ m[/tex]
[tex]\nu=1.24\times 10^{18}\ s^{-1}[/tex]
Explanation:
The expression for the deBroglie wavelength is:
[tex]\lambda=\frac {h}{m\times v}[/tex]
Where,
[tex]\lambda[/tex] is the deBroglie wavelength
h is Plank's constant having value [tex]6.626\times 10^{-34}\ Js[/tex]
m is the mass of electron having value [tex]9.11\times 10^{-31}\ kg[/tex]
v is the speed of electron.
Given that v = c / 100
Where, c is the speed of light having value [tex]3\times 10^8\ m/s[/tex]
Thus, v = [tex]\frac {3\times 10^8}{100}\ m/s=3\times 10^6\ m/s[/tex]
Applying in the equation as:
[tex]\lambda=\frac {h}{m\times v}[/tex]
[tex]\lambda=\frac {6.626\times 10^{-34}}{9.11\times 10^{-31}\times 3\times 10^6}\ m[/tex]
[tex]\lambda=\frac{10^{-34}\times \:6.626}{10^{-25}\times \:27.33}\ m[/tex]
[tex]\lambda=\frac{6.626}{10^9\times \:27.33}\ m[/tex]
[tex]\lambda=2.42\times 10^{-10}\ m[/tex]
Also,
[tex]\nu=\frac {c}{\lambda}[/tex]
So,
[tex]\nu=\frac {3\times 10^8}{2.42\times 10^{-10}}\ s^{-1}[/tex]
[tex]\nu=\frac{10^{18}\times \:3}{2.42}\ s^{-1}[/tex]
[tex]\nu=1.24\times 10^{18}\ s^{-1}[/tex]
