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melomori [17]
3 years ago
15

The x coordinate of an electron is measured with an uncertainty of 0.200 mm . What is vx, the x component of the electron's velo

city, if the minimum percentage uncertainty in a simultaneous measurement of vx is 1.00 % ? Use the following expression for the uncertainty principle:
ΔxΔpx≥ℏ,

where Δx is the uncertainty in the x coordinate of a particle, Δpx is the particle's uncertainty in the x component of momentum, and ℏ=h2π, where h is Planck's constant.

Express your answer in meters per second to three significant figures.
Physics
1 answer:
Vikentia [17]3 years ago
8 0

Answer:

Velocity of electron along x direction is 57.9 m/s

Explanation:

The uncertainty in x coordinate of electron, Δx = 0.200 mm = 0.2 x 10⁻³ m

Let vₓ be the x component of electrons velocity.

The uncertainty in x component of electrons momentum is:

Δpₓ = mΔvₓ

Here m is mass of the electron.

The uncertainty in velocity x component is 1% i.e. 0.01.

So, the above equation can be written as :

Δpₓ = 0.01mvₓ    ....(1)

The minimum uncertainty principle is:

\Delta x\Delta p_{x} = \frac{h}{2\pi }    ....(2)

Here h is Planck's constant.

From equation (1) and (2),

\Delta x\times0.01m v_{x} = \frac{h}{2\pi }

Substitute 0.2 x 10⁻³ m for Δx, 9.1 x 10⁻³¹ kg for m and 6.626 x 10⁻³⁴ m²kg/s in the above equation.

0.2\times10^{-3} \times0.01\times9.1\times10^{-31}\times v_{x} = \frac{6.626\times10^{-34} }{2\pi }

vₓ = 57.9 m/s

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Answer:

In order of increasing wavelength, the answer is:

(i) The gamma rays produced by a radioactive nuclide used in medical imaging

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From explained above, you can conclude that there is a proportionality relationship between the wavelength and the frequency, they are inversely proportional. That means: the highest frequency will have the shortest wavelength and vice-versa.

So, you have the following types:

(i) The gamma rays produced by a radioactive nuclide used in medical imaging

Frequency : Typically greater than 10^{19} Hz

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Frequency: 93.1 MHz

(iii) A radio signal from an AM radio station at 680 kHz on the dial

Frequency: 680 kHz

(iv) The yellow light from sodium-vapor streetlights

Frequency: Visible spectrum of approx. 508 - 526 THz

(v) The red light of a light-emitting diode, such as in a calculator display

Frequency: Visible spectrum of approx. 400 - 484 THz

Then, you have to organize them from the highest frequency to the smallest one (decreasing frequency), and as the highest frequency will have the shortest wavelength, you are going to have it organized in an increasing wavelength mode.

Then in order of increasing wavelength, the answer will be:

                                           (i) , (iv), (v), (ii), (iii)

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