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Chapter 8: Problem 72

Identify the orbital that has (a) two radial nodes and one angular node; (b) five radial nodes and zero angular nodes; (c) one radial node and four angular nodes.

Short Answer

Expert verified
The orbitals are: (a) 3p; (b) 5s; (c) 5f

Step by step solution

01

Identify the Orbital in case (a) two radial nodes and one angular node.

For this case, since there are two radial nodes and one angular node, the total number of nodes or 'n', will be the sum of these two giving 'n' = 3. Also, for one angular node, the orbital must be of 'p type' which is denoted as 'l = 1'. Therefore, the orbital can be identified as '3p'.
02

Identify the Orbital in case (b) five radial nodes and zero angular nodes.

For this case, since there are five radial nodes and zero angular nodes, the total number of nodes or 'n', will be the sum of these two giving 'n' = 5. And for zero angular nodes, the orbital must be of 's type' which is denoted as 'l = 0'. Therefore, the orbital can be identified as '5s'.
03

Identify the Orbital in case (c) one radial node and four angular nodes.

For this case, since there is one radial node and four angular nodes, the total number of nodes or 'n', will be sum of these two giving 'n' = 5. And for four angular nodes, the orbital must be of 'f type' which is denoted as 'l = 3'. Therefore, the orbital can be identified as '5f'.

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Most popular questions from this chapter

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.

Infrared lamps are used in cafeterias to keep food warm. How many photons per second are produced by an infrared lamp that consumes energy at the rate of \(95 \mathrm{W}\) and is \(14 \%\) efficient in converting this energy to infrared radiation? Assume that the radiation has a wavelength of \(1525 \mathrm{nm}\).

Use the Balmer equation (8.2) to determine (a) the frequency, in \(s^{-1}\), of the radiation corresponding to \(n=5\) (b) the wavelength, in nanometers, of the line in the Balmer series corresponding to \(n=7\) (c) the value of \(n\) corresponding to the Balmer series line at \(380 \mathrm{nm}\)

What type of orbital (i.e., \(3 s, 4 p, \ldots)\) is designated by these quantum numbers? (a) \(n=5, \ell=1, m_{\ell}=0\) (b) \(n=4, \ell=2, m_{\ell}=-2\) (c) \(n=2, \ell=0, m_{\ell}=0\)

A line is detected in the hydrogen spectrum at \(1880 \mathrm{nm}\). Is this line in the Balmer series? Explain.
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