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The probability of finding out an electron at a point within an atom is proportional to the
  • a)
    square of the orbital wave function i.e., ψ2
  • b)
    orbital wave function i.e., ψ
  • c)
    Hamiltonian operator i.e., H
  • d)
    principal quantum number i.e., n
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The probability of finding out an electron at a point within an atom i...
ψ2 is known as probability density and is always positive. From the value of ψat different points with in an atom it is possible to predict the region around the nucleus where electron will most probably be found.
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Most Upvoted Answer
The probability of finding out an electron at a point within an atom i...
|Ψ|^2
b) amplitude of the orbital wave function i.e., Ψ
c) product of the orbital wave function and its complex conjugate i.e., Ψ*Ψ
d) difference of the orbital wave function and its complex conjugate i.e., Ψ-Ψ*
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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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The probability of finding out an electron at a point within an atom is proportional to thea)square of the orbital wave function i.e., ψ2b)orbital wave function i.e.,ψc)Hamiltonian operator i.e., Hd)principal quantum number i.e., nCorrect answer is option 'A'. Can you explain this answer?
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