An electron is confined to a linear region w ith a lengthof the same order as the diameter of an atom (taken as100 pm). Calculate the minimum uncertainties in its positionand speed.

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

A: Probability of particle in a length L is equal to,

Q: For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell…

A:

Q: What is the probability of find ing the electron in a volume of 6.5 pm3 centred on the nucleus in…

A: a) The probability of finding the electron in 6.5 pm3 of hydrogen atom is determined as,

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: (c) Estimate the wavelength of electrons that have been accelerated from rest through a potential…

A:

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

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Q7: Quantum chemistry

A: The term commutator operator in quantum mechanics is used to tell whether two observables can be…

Q: Normalize the wavefunction, Y = Asin(2x),x = 0 to 2n. Refer to a table of integral if %D necessary.

A:

Q: An electron is confined to a linear region with a length of the same order as the diameter of an…

A: The expression for Heisenberg’s uncertainty principle is as follows,…

Q: 8.11a Confirm that the operator i = (h/i)d/dø, where ø is an angle, is hermitian.

A:

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

A:

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

A: de Broglie gave the hypothesis that all matter in this universe have dual nature i.e. both particle…

Q: By considering the integral ∫02π ψ*ml ψml dϕ, where ml≠m'l, confirm that wavefunctions for a…

A: The expression for the wave function of a particle in a ring is as follows,

Q: Consider the following two systems: (a) an electron in a onedimensional box of length 1.0 Å and (b)…

A: (a)For an electron in a 1-D box, the length of the box is: The energy of the n energy levels can be…

Q: Calculate the probability that an electron wi ll be found (a)between x= 0.1 and 0.2 nm, (b) between…

A:

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

A: De broglie wavelength is given by the formula :                            λ=hmvwhere λ is the…

Q: a. Find the average position on the x-axis, , for the wavefunction of a 2D particle in a box where…

A: Formula to calculate average value of position is

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: Normalize (to 1) the wavefunction e-ax^2 in the range −∞ ≤ x ≤ ∞, with a > 0. Refer to the…

A: Given: The wavefunction is e-ax^2  The range is −∞ ≤ x ≤ ∞ and  a > 0.

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…

A:

Q: Calculate the freqwency of wavelength radiation with a of 495nm

A: Given that , Wavelength of radiation = 495 nm = 495 x 10-7 cm Speed of light = C = 3 x 1010 cm/sec

Q: Suppose that you designed a spacecraft to work by photon pressure. The sai l was a completely…

A:

Q: 5.) Calculate the energy of separation of Ir (2) and √ (3), (1, 2) and (2, 2), I (1,1,2) and I…

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Q: By differentiation of the 3s radial wavefunction, show that it has three extrema in its amplitude,…

A: The radial wavefunction of 3s is given by, ⇒R3,0=A6-2ρ+19ρre-ρ6 where, ρ=2Zra0   On differentiating…

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

A: Given  Information - speed of proton = 0.45 Mm s-1 uncertainity in momentum = 0.0100 % = 0.0001 To…

Q: 5. Consider a particle constrained to move in one dimension described by the wavefunction v (x) =…

A: We have been a particle constrained to move in one dimension described by the given wavefunction. We…

Q: . Determine the normalized form of the wavefunction p = (2 - r/ao) e-¹/2ao

A: The precise location of an electron in an atom is difficult to determine because it is always…

Q: A nitrogen molecule is confined in a cubic box of volume 1.00 m3. (i) Assuming that the molecule has…

A: We have value for volume =1.00 m3Translational energy =32kTE -Translational energyk  -Boltzmann…

Q: How many spherical nodal surfaces are there in 4s – sub-shell?

A:

Q: What is the magnitude of the angular momentum of a CH4 molecule when it is rotating with its minimum…

A: Known details, The minimum energy to rotate = 2.11×10–22J Moment of Inertia is 5.27 × 10-47 kg m2

Q: A hydrogen atom. treated as a point mass. is confined to a one-dimensional square well of width 1.0…

A:

Q: Determine the maximum wavelength of the following molecules. a) b) Ø Br O

A: We would make use of Woodward rules to determine the maximum wavelength here.

Q: The accompanying drawingshows a contour plot for a dyzorbital. Consider the quantumnumbers that…

A: a)  The orbital shown is a d orbital which starts with n = 3 principal shell. Thus, the smallest…

Q: 421) The moment of inertia of an SF, molecule is 3.07 x 10 kg m. What is the minimum energy needed…

A: Given, the moment of inertia of an SF6 molecule = 3.07×10-45 kg m2 The minimum energy needed to…

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: In the octatetraene (C8H10) molecule, what should be the length of the electromagnetic wave required…

A: Linear chain of hydrocarbons containing conjugated pi bonds can be considered as 1D box of quantum…

Q: Calculate an approximate ground-state energy of the hydrogen atom using 1 function o(r) = re-ar,…

A:

Q: Which of these wavefunctions are normalizable over their intervals? Normalize those that can be…

A: Given:-

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

A:

Q: True or false: 1. Tunneling is more likely to contribute to reactions involving electron transfer…

A: Quantum mechanical tunneling is the phenomenon in which particles can penetrate through the…

Q: One mole of photons at wavelength 650. nm has of energy. 184 kI

A:

Q: The accompanying drawingshows a contour plot for a dyzorbital. Consider the quantumnumbers that…

A: Contour plots for any of the orbitals are basically the quantum mechanical treatment for them.

Q: 0/13/Pind the diffrence energy (AE)of particle inOz-Dard@2-D boxes with Same Leng th (L? in Second…

A: We have given that  find the difference in second and first excited state energy (∆E) of particle in…

Q: An electron is confined to a linear region w ith a length of the same order as the diameter of an…

A: The expression for Heisenberg’s uncertainty principle is as follows, Where, delta p is the…

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.