A glow-worm of mass 5.0 g emits red light (650 nm) with a power of 0.10 W entirely in the backward direction. To what speed will it have accelerated after 10 y if released into free space and assumed to live?

Q: For a particle in the stationary state n of a one dimensional box of length a, find the probability…

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Q: P= D„Ðx= (-in- Assume that -in- dx dx dx2 Evaluate for a particle in a box with 0 =m?v² h?n? II

A: This question comes under quantum mechanics and the topic is evaluation of average value for…

Q: Vanadium tetrachloride (VCl4 ) is a bright red colored liquid with a vapor pressure of 5x10-2 torr…

A: The orbital angular momentum of electron inn a given orbital is calculated by using the following…

Q: Construct the potential energy operator of a particle with potential energy V(x)=1/2kfx2, where kf…

A: The information about the location of a particle is given by Born interpretation of the wave…

Q: For a particle in a box of length L and in the state with n = 3, at what positions is the…

A: The wavefunction does not describe exact location of the microscopic particle. It tells about…

Q: If we have two operators Ậ = x and Ê = d/dx and a function f(x) = x². Clearly indicate if these two…

A: If two operator commute then AB=BA,where A,B are two operator.

Q: Calculate the expectation values of x and x2 for a particle in the state with n = 1 in a…

A: The expectation value of x2 for a particle is given by following expression. The value of ψ for one…

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

A: Given: The wave function is as follows,

Q: The kinetic energy of an electron is (Z + 1.5)keV. momentum of the electron.

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Q: The rotation of a molecule can be represented by the motion of a particle moving over the surface of…

A: Value of angular momentum quantum no, l = 1 Calculation of angular momentum, L: where h/2Π is ħ…

Q: the lifetime of the 4p1/2 state of potassium, is 27.3 ns. what are the einstein a and b coefficients…

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Q: Normalize the wave function ψ= A sin (nπ/a x) by finding the value of the constant A when the…

A: Normalization is the scaling of wave functions so that all the probabilities add to 1.

Q: Define, justify, and provide examples of zero-point energy.

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Q: For a particle in a cubic box of edge a; (a) How many states have energies in the range 0 to…

A: Solution :     For a particle in a cubic box of edge length a, Energy is given by…

Q: 3. Plot the eigenstate and particle probability for a particle in a box, with infinite height walls,…

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Q: What values of J may occur in the terms (i) 1S, (ii) 2P, (iii) 3P? How many states (distinguished by…

A: Term symbol represents the abbreviated form of total angular momentum in a multi electron system.…

Q: 4. Given these operators A=d/dx and B=x², can you measure the expectation values of the…

A: We have to use the concept of commutator over here. If the given observable commute with each other,…

Q: The Hamiltonian operator y for the harmonic oscillator is given by Ĥ = - a h? d? + suw? â?, where l…

A: Given: Hamiltonian operator H^=-ℏ22μd2 dx2+12μω2x^2 μ is the reduced mass ω=2πν is the angular…

Q: Where are the nodes in the wavefunction for a particle confined to a box with 0 < x < a and n=3?

A: Wave function for a particle in a box with 0 &lt; x &lt; a and n=3 No of nodes = to be determined.…

Q: If a nitrogen molecule is trapped in a hypothetical 1-D box of length 1.10 cm, at what value of the…

A: Translational energy :-            It is the energy which is associated with displacement of a…

Q: For a system consisting of three particles in 3D, on what variables does the time-independent wave…

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Q: Consider a hydrogen atom in the 1s state. (a) For what value of r is the potential energy U(r) equal…

A: Generally, the hydrogen atom in the 1s state consists of one electron in the orbital. The value of r…

Q: 4. A quantum simple harmonic oscillator can be treated as a particle of mass m attached to a spring…

A: Concept:  Energy of quantum simple hormonic oscillator:    E = (n+1/2)hv  Where  E = energy  n =…

Q: For a system of two non-interacting particles of mass 9.0 x 10-26 g and 5.0×10-26 g in a one…

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Q: Draw scale vector diagrams to represent the states (i) l = 1, ml = +1, (ii) l = 2, ml = 0.

A: The vector  diagrams to represent the states (i) l = 1, ml = +1 has to be given, i) The vector…

Q: The moment of inertia of a CH4 molecule is 5.27 × 10−47 kg m2. What is the minimum energy needed to…

A: The energy levels derived for the rotation in three dimension are E = l(l+1)h22I Where l. = 0, 1,2

Q: Identify the normalized wavefunction for a particle rotating about the surface of a sphere with a…

A: Given : Spherical surface and spherical particles. To find : Normalized wave function.  Solution :…

Q: Imagine a particle free to move in the x direction. Which of the following wavefunctions would be…

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Q: Evaluate the following commutators d @[4] (a) x, dx d (b) x, [x [*] dy d (c) dx - x₂ d dx + x

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Q: Without evaluating any integrals, state the value of the expectation value of x for a particle in a…

A: The probability density, ψ2, is symmetrical about x=l2. Therefore, it can be stated that probability…

Q: Evaluate the linear momentum and kinetic energy of a free electron described by the wavefunction…

A: In a matter wave, the possibility of finding an electron is called wave function. Basically, wave…

Q: The operator (x+d/dx) has the eigen value α. Determine the corresponding wave function

A: If we let the eigen function is f(x) and eigen operator is ( x +d/dx ) having eigen value α, then we…

Q: The energy required for the excitation from the 2nd to the 3rd excited levels in a particle moving…

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Q: 09) What is the degree of the degeneracy of a state You for a particle confined in cubic box A)1 B)…

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Q: What are the  Probability Densities?

A: In probability theory, a probability density function, or density of a continuous random variable,…

Q: What are the dimensions of a wavefunction that describes a particle free to move in both the x and y…

A: The wave function t of the particle in a two-dimensional box is as follows:

Q: For a particle in one-dimensional box of length a, y, = ax(a – x) and yw2 = x(a – x)(a + x) can each…

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Q: Consider a single particle with rest mass m residing in a one-dimensional space, x. = o for x a,…

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Q: 6) The relation between the kinetic energy and linear momentum can be expressed by the following…

A: Given Kinetic Energy  Relation between Kinetic Energy and momentum = ?

Q: (a) For a particle in the stationary state n of a one dimensional box of length a, find the…

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

Q: Confirm that the wavefunction Y(x,t)= e(px-Et)/h is a solution of the one-dimensional time- 2.…

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Q: 3.2 Consider an assembly of six indistinguishable particles obeying Bose-Einstein statistics. The…

A: The solution of the given question is

Q: Find the uncertainty ox in x as a function of the uncertainties ou and oy in u and v for the…

A: Solution.                       Given that (a) x = 1/2(u + v) (b) x = uv^2 (c) x = u^2+v^2

Q: The velocity (m/s) of an electron with a de Broglie wavelength of 1.312 nm is:

A: De-Broglie wavelength of any particle is given by λ=hmv  ;  h = Plancks constant m =mass of electron…

Q: Which of these choices is the expectation value of momentum p for a particle in the state n = 5 in a…

A: The reasonable expected value of the result of an experiment is known as its expected value.

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.