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An electron of a velocity 'x' is found to have a certain wavelength. The velocity to be possessed by the neutron to have half the de Broglie wavelength possessed by electron is. A) x/1840. B) x/920. C) 3680x. D) x/3680?
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An electron of a velocity 'x' is found to have a certain wavelength. T...
Explanation:


De Broglie wavelength:


De Broglie wavelength is the wavelength associated with the motion of a particle. It is given by the formula:

λ = h/p

Where λ is the wavelength, h is the Planck's constant, and p is the momentum of the particle.

Relation between velocity and momentum:


The momentum of a particle is related to its velocity by the formula:

p = mv

Where p is the momentum, m is the mass of the particle, and v is the velocity of the particle.

Calculating the velocity of the neutron:


We are given the velocity of the electron and the wavelength associated with its motion. We need to find the velocity of the neutron that would have half the de Broglie wavelength of the electron.

Let the velocity of the neutron be v_n. Then, we can write:

λ_n/2 = h/p_n

Where λ_n/2 is half the de Broglie wavelength of the electron, and p_n is the momentum of the neutron.

We can also write:

p_n = mv_n

Substituting the second equation into the first equation, we get:

λ_n/2 = h/mv_n

Simplifying this equation, we get:

v_n = h/(mλ_n/2)

We know that the de Broglie wavelength of the electron is given by:

λ_e = h/mev_e

where me is the mass of the electron.

Substituting this equation into the previous expression for v_n, we get:

v_n = h/(mλ_e/4)

Simplifying this equation, we get:

v_n = 4hv_e/(mλ_e)

Now, we can substitute the given value of v_e and solve for v_n:

v_n = 4hv_e/(mλ_e) = 4h(x)/(meλ_e) = (4/1840)x

Therefore, the velocity of the neutron that would have half the de Broglie wavelength of the electron is x/920, which is option (B).

Answer: B) x/920.
Community Answer
An electron of a velocity 'x' is found to have a certain wavelength. T...
Is the answer is X/920...!am i right?✌
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Read the following text and answer the following questions on the basis of the same:Electron Microscope Electron microscopes use electrons to illuminate a sample. In Transmission Electron Microscopy (TEM), electrons pass through the sample and illuminate film or a digital camera.Resolution in microscopy is limited to about half of the wavelength of the illumination source used to image the sample. Using visible light the best resolution that can be achieved by microscopes is about ~200 nm. Louis de Broglie showed that every particle or matter propagates like a wave. The wavelength of propagating electrons at a given accelerating voltage can be determined byThus, the wavelength of electrons is calculated to be 3.88 pm when the microscope is operated at 100 keV, 2. 74 pm at 200 keV and 2.24 pm at 300 keV. However, because the velocities of electrons in an electron microscope reach about 70% the speed of light with an accelerating voltage of 200 keV, there are relativistic effects on these electrons. Due to this effect, the wavelength at 100 keV, 200 keV and 300 keV in electron microscopes is 3.70 pm, 2.51 pm and 1.96 pm, respectively.Anyhow, the wavelength of electrons is much smaller than that of photons (2.5 pm at 200 keV). Thus if electron wave is used to illuminate the sample, the resolution of an electron microscope theoretically becomes unlimited. Practically, the resolution is limited to ~0.1 nm due to the objective lens system in electron microscopes. Thus, electron microscopy can resolve subcellular structures that could not be visualized using standard fluorescence microscopy.Q. Wavelength of electron as wave at accelerating voltage 200 keV is

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An electron of a velocity 'x' is found to have a certain wavelength. The velocity to be possessed by the neutron to have half the de Broglie wavelength possessed by electron is. A) x/1840. B) x/920. C) 3680x. D) x/3680?
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An electron of a velocity 'x' is found to have a certain wavelength. The velocity to be possessed by the neutron to have half the de Broglie wavelength possessed by electron is. A) x/1840. B) x/920. C) 3680x. D) x/3680? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about An electron of a velocity 'x' is found to have a certain wavelength. The velocity to be possessed by the neutron to have half the de Broglie wavelength possessed by electron is. A) x/1840. B) x/920. C) 3680x. D) x/3680? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electron of a velocity 'x' is found to have a certain wavelength. The velocity to be possessed by the neutron to have half the de Broglie wavelength possessed by electron is. A) x/1840. B) x/920. C) 3680x. D) x/3680?.
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