(a)
Interpretation:
An expression for the total energy, E of the electron (mass me) moving in a circular orbit of radius r with speed U should be written.
Concept introduction:
An electron orbiting in a circular orbit around the nucleus experiences two types of energies. They are kinetic energy and the potential energy due to attractive forces between nucleus and electron.
(b)
Interpretation:
It should be shown that the total energy of the electron is
Concept introduction:
Electrostatic force between two charges is given by the following relation:
Here, ke − Coulomb constant
q1 and q2 − magnitude of the charges
r − distance between the two charges.
(c)
Interpretation:
It should be shown that the energy and radius of the nth orbit are respectively,
Concept introduction:
Using the condition that the force of attraction between the electron and proton has the same magnitude as the centrifugal force:
The total energy of the electron is as follows:
(d)
Interpretation:
Concept introduction:
Reduced mass can be calculated as follows:
Here,
Also,
The conversion of
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GENERAL CHEMISTRY-MOD.MASTERINGCHEM.
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- The energy needed to ionize an atom of element X when it is in its most stable state is 500kJmol1 . However, if an atom of X is in its lowest excited state, only 120kJmol1 is needed to ionize it. What is the wavelength of the radiation emitted when an atom of X undergoes a transition from the lowest excited state to the ground state?arrow_forwardUse the mathematical expression for the 2pz wave function of a one-electron atom (see Table 5.2) to show that the probability of finding an electron in that orbital anywhere in the x-y plane is 0. What are the nodal planes for a dxz orbital and for a dx2y2 orbital?arrow_forwardCompare the mass of the electron, me, with a the reduced mass of a hydrogen atom; b the reduced mass of a deuterium atom (deuterium=2H); c the reduced mass of a carbon 12 atom having a +5 charge, that is, C5+. Suggest a conclusion to the trend presented by parts a-c.arrow_forward
- Consider a one-dimensional particle-in-a-box and a three-dimensional particle-in-a-box that have the same dimensions. a What is the ratio of the energies of a particle having the lowest possible quantum numbers in both boxes? b Does this ratio stay the same if the quantum numbers are not the lowest possible values?arrow_forwardThe de Broglie equation for a particle can be applied to an electron orbiting a nucleus if one assumes that the electron must have an exact integral number of wavelengths as it covers the circumference of the orbit having radius r:n=2r. From this, derive Bohrs quantized angular momentum postulate.arrow_forwardBased on the trend shown in Figure 11.5, draw the probability distribution of a harmonic oscillator wavefunction that has a very high value of n. Explain how this is consistent with the correspondence principle.arrow_forward
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