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motikmotik
3 years ago
14

What is the de Broglie wavelength of an electron that strikes the back of the face of a TV screen at 1/10 the speed of light? __

___m
Physics
1 answer:
Softa [21]3 years ago
6 0

Answer: 2.42(10)^{-11} m

Explanation:

The de Broglie wavelength \lambda is given by the following formula:

\lambda=\frac{h}{p}   (1)

Where:

h=6.626(10)^{-34}\frac{m^{2}kg}{s} is the Planck constant

p is the momentum of the atom, which is given by:

p=m_{e}v_{e}   (2)

Where:

m_{e}=9.11(10)^{-31}kg is the mass of the electron

v=\frac{1}{10}c is the velocity of the electron (we are told it is 1/10 the speed of light c=3(10)^{8}\frac{m}{s})

This means equation (2) can be written as:

p=m_{e}\frac{1}{10}c   (3)

Substituting (3) in (1):

\lambda=\frac{h}{m_{e}\frac{1}{10}c}    (4)

\lambda=10\frac{h}{m_{e} c}    (5)

Now, we only have to find \lambda:

\lambda=10\frac{6.626(10)^{-34}\frac{m^{2}kg}{s}}{(9.11(10)^{-31}kg)(3(10)^{8}\frac{m}{s})}     (6)

<u>Finally:</u>

\lambda=2.42(10)^{-11} m>>> This is the de Broglie wavelength of an electron.

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