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Chapter 8: Problem 14

What is \(\Delta E\) for the transition of an electron from \(n=5\) to \(n=2\) in a Bohr hydrogen atom? What is the frequency of the spectral line produced?

Short Answer

Expert verified
To find \(\Delta E\), calculate the energies at each state, and subtract \(E_5\) from \(E_2\). To find the frequency, use the derived \(\Delta E\) value and apply the equation \(E=h\nu\). Remember to convert \(\Delta E\) from eV to Joules before calculating the frequency.

Step by step solution

01

Calculation of energies in different orbitals

Calculate the energies in both states using the equation \(E=-13.6/n^2\). Substitute \(n=5\) to find \(E_5\), and \(n=2\) to find \(E_2\). The energies are in electron volts (eV).
02

Calculation of the Energy difference

Determine the difference in energy levels. The energy difference \(\Delta E = E_2 - E_5\).
03

Convert energy difference to Joules

The resulting energy difference will be in electron volts. Convert this value to joules using the conversion factor \(1 eV = 1.6 x 10^{-19} J \) to use in the next step.
04

Calculation of spectral line frequency

Having gotten \(\Delta E\) in joules, use it to calculate the frequency of the spectral line produced using the relation \(E=h\nu\), where \(h\) is Planck's constant \((6.62607004 × 10^-34 m^2 kg / s)\). Solve for \(\nu\) by dividing \(\Delta E\) by \(h\)

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Most popular questions from this chapter

In the ground state of a hydrogen atom, what is the probability of finding an electron anywhere in a sphere of radius (a) \(a_{0},\) or \(\left(\text { b) } 2 a_{0} ?\right.\)

For electromagnetic radiation transmitted through a vacuum, state whether each of the following properties is directly proportional to, inversely proportional to, or independent of the frequency: (a) velocity; (b) wavelength; (c) energy per mole. Explain.

Electromagnetic radiation can be transmitted through a vacuum or empty space. Can heat be similarly transferred? Explain.

Show that the probability of finding a \(2 p_{y}\) electron in the \(x z\) plane is zero.

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