A particle is confined to a 1D box between r = 0 and a =1. Suppose the normalized wave function of the particle is V (x) = ÷(x+1) for 0 < ¤ <1 and zero everywhere else. Find N, assuming that N is a positive number.

Q: Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the…

A: Speed of electron and wavelength are linked to each other as follows:

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Q: Show that the third Bohr postulate, Eq. (2–5), is equivalent to an integer num- ber of de Broglie…

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Q: For the system described in Exercise E7B.1(a) (A possible wavefunction for an electron in a region…

A: Here in question exercise is not mentioned, so here assume particle in 1-D box system. When mod…

Q: Consider a particle trapped in a iD box with zero potential energy with walls at x = 0 and x = L.…

A: Here we have toapply probability formula

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A: Quantum energy involved in the excitation : i) An electron have oscillation period =2.50 fs.  Then…

Q: Calculate the probability that a particle will be found between 0.49L and 0.51L in a box of length L…

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Q: (a) What is the lowest possible value of the principal quantum number (n) when the angular momentum…

A: There are four types of quantum numbers: Principle quantum number (n) Azimuthal quantum number (l)…

Q: Normalize (to 1) the wavefunction e–ax in the range 0 ≤ x ≤ ∞, with a &gt; 0.

A: Given: The wave function is as follows,

Q: P7B.8 A normalized wavefunction for a particle confined between 0 and L in the x direction, and…

A: Given: The probability of finding the particle between x1 and x2 along the x-axis and between y1 and…

Q: The radial wave function of a quantum state of Hydrogen is given by R(r)= (1/[4(2π)^{1/2}])a^{-3/2}(…

A:

Q: The normalized wave function for a particle in a one- dimensional box in which the potential energy…

A:

Q: 1/x be normalized

A:

Q: Which of the following wavefunctions are eigenfunctions of the operator

A:

Q: The radial eigenfunction for the quantum state of lowest energy for an electron with angular…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: At what radius does the probability density of an electron in the H atom fall to 50 per cent of its…

A:

Q: (iii) Show that the wave function of the particle in the potential well is NA X w.(x) = C sin n =…

A:

Q: Calculate the expectation value of the radius (r) at which you would find the electron if the H atom…

A:

Q: What is the frequency of a photon resulting from the transition of n = 6 → n = 1 ? (give answer to 3…

A: Given information,Photon resulting from the transition of n = 6 to n = 1.Use Rydberg’s formula,

Q: What is the lowest possible value of the principal quantum number (1) when the angular momentum…

A:

Q: Functions of the form sin(nπx/L), where n = 1, 2, 3 …, are wavefunctions in a region of length L…

A: The wavefunction is given as,ψ = sin nπxLFor n=1,     ψ1 = sin πxLFor n=2,     ψ1 = sin 2πxL

Q: P7D.8* A particle is confined to move in a one-dimensional box of length L. If the particle is…

A: a.

Q: b) Consider the function of 4(x) = c sin 2nx +d sin Explain if Y(x) is an acceptable wave function…

A:

Q: The speed of a certain proton is 0.45 Mm s−1. If the uncertainty in its momentum is to be reduced to…

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Q: For a particle in a one- dimensional box, the ground state wavefunction is W = ( 2/a)1/2 sin Tx/a…

A: Given  Type of box = 1-D box  Region range = L4 to 3L4  Probability of finding the particle in a box…

Q: How many possible values of angular momentum quantum number l are there in the shell with n = 4?

A: The 4 quantum numbers are  1) Principal quantum number (n) = shell number or orbit number  2)…

Q: Heisenberg's uncertainty principle can be expressed mathematically as Δx*Δp = h/4π, where Δx and Δp…

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Q: What is the average position of a harmonic oscillator with n = 1? (Hint: Your knowledge of odd and…

A: The answer is given as follows

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Q: calculate the de Broglie wavelength of electrons accelerated through 50kV. (b) Is the relativistic…

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Q: To what speed must a proton be accelerated from rest for it to have a de Broglie wavelength of 100…

A: Given: Wavelength = 100 pm or 1×10-10 m The de Broglie wavelength is given by the expression: λ = hp…

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A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Determine y y for each of the following wavefunctions: (i = -1) a) y(x) = ek b) y(0) = sin 0 +i cose…

A:

Q: What is the lowest possible value of the angular momentum quantum number (l) when the magnetic…

A: Value of magnetic quantum number depends on the value of azimuthal quantum number (l).

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Q: 4) For a particle in a 1-D box where the particle in confined between z = 0 and z = a, if the…

A:

Q: Calculate the wavelength of the photon needed to excite a transition between neighbouring energy…

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Quantum Chemistry

Quantum chemistry deals with the properties of chemical systems and their reactions. The branch of chemistry which is more concerned with quantum chemistry is physical chemistry. It is a more sophisticated field of theoretical physics which is concerned towards the application of physical concepts towards various chemical aspects such as, formation of atoms, chemical structure descriptions, chemical bond strength, hybridization, conjugation etc. Quantum chemistry mainly studies the various states i.e., ground state, excited state, transition states of the individual atoms or molecules taking place during any chemical reaction. The laws of motion explained by various scientists, which are termed as “classical mechanics” were not acceptable in terms of electrons, protons, atoms, light etc. Thus, a new theory named “quantum mechanics” emerged to understand the basic framework of various atomic and subatomic particles.