An electron is confined to a square well of length L. What would be the length of the box such that the zero-point energy of the electron is equal to its rest mass energy, mec2? Express your answer in terms of the parameter λC = h/mec, the ‘Compton wavelength’ of the electron.

Q: A glow-worm of mass 5.0 g emits red light (650 nm) with a power of 0.10 W entirely in the backward…

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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:

Q: To what speed must a proton be accelerated for it to have a de Broglie wavelength of 3.0 cm?

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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: Ultraviolet light with a wavelength of 400 nm falls on a specific metal surface. The maximum value…

A: When a radiation of high frequency, high energy is incident on the metal surface then some free…

Q: Calculate the energy of the quantum involved in the excitation of (i) an electronic oscillation of…

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

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

A: The probability of finding the electron in the range dx at x = L/6 is calculated by the following…

Q: A sodium lamp emits yellow light (550 nm). How many photons does it emit each second if its power is…

A: Given: A sodium lamp emits yellow light 550 nm Calculation: The power and number of photons are…

Q: The speed of a certain electron is 995 km s−1. If the uncertainty in its momentum is to be reduced…

A: According to Heisenberg’s uncertainty principle, if the accurate momentum of particle is known, its…

Q: The ground-state wavefunction for a particle confined to a one dimensional box of length L is Ψ…

A: Ans.

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

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Q: Consider a collection of 10,000 atoms of rubidium-87, confined inside a box of volume (10-5 m)3.…

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Q: The wavefunction of one of the d orbitals is proportional to sin2θ sin 2ϕ. At what angles does it…

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Q: What is (a) the energy. (b) the speed of an electron that has been ejected from an orbital of…

A: a) The expression required to determine the energy is as follows, The calculation is as follows,

Q: For an electron having a one-dimensional wavefunction Y = √√2π sin x in the range x = 0 to 1 what is…

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Q: Consider a particle trapped in a 1D box with zero potential energy with walls at x = 0 and x = L.…

A: Potential energy (V) is the energy possessed by the electron or any object due to its position which…

Q: What is the energy (in kl) of 1 mole of yellow photons of wavelength 275 nm?

A: We first calculate the energy for one photons. Then this value will be multiplied by 6.023 x 1023 to…

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

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

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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: A possible wavefunction for an electron in a region of length L (i.e. from x=0 to x=L) is 2 πχ. sin…

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Q: What is the probability (between 0 and 1) of finding an electron in the 1s state of hydrogen at a…

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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: For the same system as in Exercise E7C.3(a) (Functions of the form sin(nπx/L), where n = 1, 2, 3 …,…

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Q: What is the numerical probability of finding an electron in a box of length L between 0 and L/4 when…

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Q: Use the Rydberg equation 1/λ= R(a1/n₁²-1/n₂²) to calculate the energy difference (E) for the…

A: The expression of energy in terms of Rydberg constant can be given as, E=hcR1n12-1n22 where 1…

Q: At what speed is an electron's de Broglie wavelength 1.03nm? At what speed is an electron's de…

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

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Q: Determine the energetic difference between state n = 2 and n = 1 for a proton in a one-dimensional…

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Q: Suppose that a proton of an acidic hydrogen atom is confined to an acid that can be represented by a…

A: We have a proton of an acidic hydrogen atom which is confined to the acid that can be represented by…

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

A: Electrons have a rest mass, unlike photons, they have a de Broglie wavelength which is really…

Q: 1. Calculate the frequency and the energy of a mole of photons associated with an electromagnetic…

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Q: 1. The workfunction (0) of platinum is 5.65 eV (1 eV = 8,064 cm' = 1.602 x 1019 J). What is the…

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Q: If an electron confined to a potential well of width 1.40 nm with infinite barriers on both sides…

A: Given data:

Q: Calculate the probability that a particle will be found in a tiny slice of space between 0.49L and…

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Q: How fast would a particle of mass 1.0 g need to travel to have the same linear momentum as a photon…

A: According to De-Broglie wavelength is given by, λ=hmv where h is the Plank's constant, m is the mass…

Q: 7A.1(b) Calculate the size of the quantum involved in the excitation of (i) an electronic…

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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: What values of J may occur in the terms (i) 3D, (ii) 4D, (iii) 2G? How many states (distinguished by…

A: A term symbol is represented as 2S+1LJ J can take the values from L+S to L-S L = 0 for S  L = 1 for…

Q: Calculate the wavelength for the transition between state with N=3, I=2,M1=0 and state with n=2,…

A: Given that, transition between two states; The first state n1 = 3  and I = 2, M1 = 0 The second…

Q: A particle rotating on the surface of a sphere with fixed r has the quantum numbers I = 3 and mj =…

A: The answer is given as follows The orbital angular momentum of the rotating particle is given by the…

Q: Calculate the wavelength of light emitted as an electron undergoes a transition from level n= 110 to…

A: Given that: ninitial = 109 nfinal = 110 To calculate:  wavelength of light emitted? region of…

Q: Neutrons, like electrons and photons, are particle-waves whose diffraction patterns can be used to…

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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.