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Chapter 40: Q2P (page 1247)

How many electron states are there in a shell defined by the quantum number n = 5 ?

Short Answer

Expert verified

There are 50 electron states in the shell defined by the quantum number n = 5 .

Step by step solution

01

The given data

The given quantum number, n = 5

02

Understanding the concept of electron states in a shell

Using the concept of possible electron states for a given quantum number, we can get the required value of the number of the electron states in a shell.

Formulae:

The number of possible electron states for each value of lis, Nl=2(2l+1) 鈥�...(颈)

The total number of possible electron states for a given n, Nn=鈭�1n-1Nl 鈥︹赌�(颈颈)

03

Calculation of the number of electron states in a shell

We know that for a given quantum number n, there are n possible values of l, ranging from 0 to (n-1) .

Thus, the total number of electron states ( ms=卤12) can be given using equation (i) in equation (ii) with the given value n = 5 as follows:

Nn=鈭�1n-122l+1=2鈭�1n-12l+1=2n2=2(5)2 =50

Hence, the total number of electron states is 50 .

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Most popular questions from this chapter

Figure 40-22 shows three points at which a spin-up electron can be placed in a non-uniform magnetic field (there is a gradient along the z-axis).

(a) Rank the three points according to the energy Uof the electron鈥檚 intrinsic magnetic dipole moment 渭s鈫�, most positive first.

(b) What is the direction of the force on the electron due to the magnetic field if the spin-up electron is at point 2?

For the situation of Problem 21, what multiple of h2/8mL2gives the energy of (a) the first excited state, (b) the second excited state, and (c) the third excited state of the system of seven electrons? (d) Construct an energy-level diagram for the lowest four energy levels of the system.

A tungsten (Z=74) target is bombarded by electrons in an x-ray tube. The K,L and M energy levels for tungsten (compare Fig. 40-15) have the energies 69.5 keV,11.3 keV, and 2.30 keV respectively. (a) What is the minimum value of the accelerating potential that will permit the production of the characteristick伪 andk尾 lines of tungsten? (b) For this same accelerating potential, what is 位min? What are the (c) k伪and (d)k尾 wavelengths?

For Problem 20, what multiple of h2/8mL2gives the energy of (a) the first excited state, (b) the second excited state, and (c) the third excited state of the system of seven electrons? (d) Construct an energy-level diagram for the lowest four energy levels.

For a helium atom in its ground state, what are quantum numbers (n,l,mI,ms) for the (a) spin-up electron and (b) spin-down electron?
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