Answer:
[tex]v = 3.65 * 10^6 m/s[/tex]
Explanation:
Given
de Broglie wavelength = 0.20nm
Required
Determine the speed (v)
The speed is calculated using the following formula;
[tex]L = \frac{h}{mv}[/tex]
Where
[tex]L = Wavelength = 0.2nm[/tex]
[tex]h = Planck's\ constant = 6.63 * 10^{-34}Js[/tex]
[tex]m = Mass\ of\ Electron = 9.11 * 10^{-31} kg[/tex]
Substitute these values in the above formula
[tex]0.2nm = \frac{6.63 * 10^{-34}}{9.11 * 10^{-31} * v}[/tex]
-----------------------------------------------------
Convert 0.2nm to metre (m)
[tex]0.2nm = 0.2 * 10^{-9}m[/tex]
-----------------------------------------------------
[tex]0.2 * 10^{-9} = \frac{6.63 * 10^{-34}}{9.11 * 10^{-31} * v}[/tex]
Multiply both sides by v
[tex]v * 0.2 * 10^{-9} = \frac{6.63 * 10^{-34}}{9.11 * 10^{-31} * v} * v[/tex]
[tex]v * 0.2 * 10^{-9} = \frac{6.63 * 10^{-34}}{9.11 * 10^{-31} }[/tex]
[tex]v * 0.2 * 10^{-9} = \frac{0.73 * 10^{-34}}{10^{-31} }[/tex]
[tex]v * 0.2 * 10^{-9} = 0.73 * 10^{-34} * 10^{31}[/tex]
Apply law of indices
[tex]v * 0.2 * 10^{-9} = 0.73 * 10^{-34 + 31}[/tex]
[tex]v * 0.2 * 10^{-9} = 0.73 * 10^{-3}[/tex]
Divide both sides by [tex]0.2 * 10^{-9}m[/tex]
[tex]v = \frac{0.73 * 10^{-3} }{ 0.2 * 10^{-9} }[/tex]
[tex]v = \frac{3.65 * 10^{-3} }{10^{-9} }[/tex]
[tex]v = \frac{3.65 * 10^{-3} }{10^{-9} }[/tex]
Apply law of indices
[tex]v = 3.65 * 10^{-3} * 10^9[/tex]
[tex]v = 3.65 * 10^{-3+9}[/tex]
[tex]v = 3.65 * 10^6[/tex]
Hence;
The velocity is
[tex]v = 3.65 * 10^6 m/s[/tex]
