A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 10¹2 per second. What is the force constant of the bonds connecting one atom with the other? (Take, molecular weight of silver = 108 and Avogadro number = 6.02 × 10²3 g mol-¹)
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![A silver atom in a solid oscillates in simple harmonic
motion in some direction with a frequency of 10¹2 per
second. What is the force constant of the bonds connecting
one atom with the other? (Take, molecular weight of silver
= 108 and Avogadro number = 6.02 × 10²3 g mol-¹)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7355c65-bc7c-48ca-a42f-5560317047c7%2F2eea408d-fd94-4f33-9fd0-b6f244cc969e%2Fawqysvl_processed.jpeg&w=3840&q=75)
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- A particle with a mass of 1.8 x 10-20 kg is oscillating with simple harmonic motion with a period of 2.2 x 10-5 s and a maximum speed of 1.9 x 10³ m/s. Calculate (a) the angular frequency and (b) the maximum displacement of the particle. (a) Number (b) Number i Units Units vQuantum mechanics is used to describe the vibrational motion of molecules, but analysis using classical physics gives some useful insight. In a classical model the vibrational motion can be treated as SHM of the atoms connected by a spring. The two atoms in a diatomic molecule vibrate about their center of mass, but in the molecule HIHI, where one atom is much more massive than the other, we can treat the hydrogen atom as oscillating in SHM while the iodine atom remains at rest. A classical estimate of the vibrational frequency is ff = 7.0×10137.0×1013 HzHz. The mass of a hydrogen atom differs little from the mass of a proton. If the HIHI molecule is modeled as two atoms connected by a spring, what is the force constant of the spring? Express your answer to two significant figures and include the appropriate units. The vibrational energy of the molecule is measured to be about 5×10−20J5×10−20J. In the classical model, what is the maximum speed of the HH atom during its SHM?…Two blocks of masses m1=1.0 kg and m2=3 kg are connected by an ideal spring of force constant k=4 N/m and relaxed length L. If we make them oscillate horizontally on a frictionless surface, releasing them from rest after stretching the spring, what will be the angular frequency ω of the oscillation? Choose the closest option. Hint: Find the differential equation for spring deformation.
- A boy of mass 49.8 kg standing on the end of a diving board depresses it vertically downward a distance of 15.7 cm. By pushing down on the board with a force a little greater than his weight, the boy can depress the end of the board a bit farther. The boy and the board then oscillate up and down. Estimate the period of oscillation, assuming that the force the board exerts is approximately like that of a compressed spring, in other words, that it obeys Hooke's law.A particle with a mass of 2.9 × 10-20 kg is oscillating with simple harmonic motion with a period of 4.7 × 10-5 s and a maximum speed of 1.8 × 103 m/s. Calculate (a) the angular frequency and (b) the maximum displacement of the particle. (a) Number i (b) Number Units UnitsA magnesium atom (mass ≈≈ 24 proton masses) in a crystal is measured to oscillate with a frequency of roughly 1014 Hz. What is the effective spring constant of the forces holding the atom in the crystal?
- The chemical bond between the two atoms in a diatomic oxygen molecule acts very much like a spring, such that each oxygen atom behaves like a simple harmonic oscillator. If we observe the oxygen atoms vibrating at a frequency of 3.0 x 10^13 Hz, what is the spring constant of the O—O bond? The mass of an oxygen atom is 2.66 x^-26 kg.In the methane molecule, CH4, each hydrogen atom is at the corner of a regular tetrahedron with the carbon atom at the center. If one of the C-H is in the direction of A=î +î+R and an adjacent C-H bond is at the direction B=î-Î-R. results to an angular bond of approximately 109° for a static frozen molecule. However, the molecule we can encounter everyday continuously vibrates and interact with the surrounding causing its bond vector to vary slightly. According to a new spectroscopy analysis, the adjacent bond vectors was found to be A = 1.06i + 0.8j + 1.03k B = 1i + -0.92j + -0.95k What is the angle (in degrees) between the bonds based on this new data? Note: Only 1% of error is permitted for the correct answer.A piston in a gasoline engine oscillates with simple harmonic motion. The displacement of the piston varies according to x(t) = (6.00 cm) cos (2t + ), where x is in cm and t is in seconds. At t= 0, find: i) the position of the particle, ii) its velocity, iii) its acceleration, iv) the period, and v) the amplitude.
- In the methane molecule, CH4, each hydrogen atom is at the corner of a regular tetrahedron with the carbon atom at the center. If one of the C-H is in the direction of A=î + Î +R and an adjacent C-H bond is at the direction B=î-1-R. results to an angular bond of approximately 109° for a static frozen molecule. However, the molecule we can encounter everyday continuously vibrates and interact with the surrounding causing its bond vector to vary slightly. According to a new spectroscopy analysis, the adjacent bond vectors was found to be A= 1.01i + 1.07j + 1.09k B = 0.92i + -1.07j + -1.04k What is the angle (in degrees) between the bonds based on this new data? Note: Only 1% of error is permitted for the correct answer.We can model a molecular bond as a spring between two atoms that vibrate with simple harmonic motion.The figure below shows an simple harmonic motion approximation for the potential energy of an HCl molecule.This is a good approximation when E < 4 ×10^−19. Since mH << mCl, we assume that the hydrogen atomoscillates back and forth while the chlorine atom remains at rest. Estimate the oscillation frequency of theHCl molecule using information in the figure below.A vertical wire 2.1m long and of 0.0042 cm2 cross sectional area has a Young’s modulus of 2.00 x 1011 Pa. A 4.0 kg object is fastened to its end and stretches the wire elastically. If the object is now pulled down a little and released, the object undergoes vertical single harmonic motion. Find the period of its vibration.