Answer:
0.213 nm
Explanation:
The equation of de Broglie that relates the energy and the wavelength is:
E = h*f
Where h is the plack constant (6.626x10⁻³⁴ J.s), and f is the frequency. The frequency is the speed of light (c) divided by the wavelength (λ).
The wavelength can be calculated then by:
λ = h/mv
Where m is the mass, and v the velocity of the particle. So:
λ = 6.626x10⁻³⁴/(9.109x10⁻³¹x3.42x10⁶)
λ = 2.13x10⁻¹⁰ m
λ = 0.213 nm
The wavelength, in nanometers, associated with the electron is 0.213 nanometers.
Given the following data:
To find the wavelength, in nanometers, associated with the electron, we would use De Broglie's equation:
Mathematically, De Broglie's equation is given by the formula:
[tex]W = \frac{h}{mv}[/tex]
Where:
Substituting the given parameters into the formula, we have;
[tex]W = \frac{6.626(10^{-34})}{9.109(10^{-31})[(3.42(10^6)]}[/tex]
Wavelength, W = × meters
Note: 1 nanometer is equal to 0.00000000001 meters
Wavelength, W = 0.213 nanometers
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