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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) …...(i)

The total number of possible electron states for a given n, Nn=∑1n-1Nl ……(ii)

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=±12) can be given using equation (i) in equation (ii) with the given value n = 5 as follows:

Nn=∑1n-122l+1=2∑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

When electrons bombard a molybdenum target, they produce both continuous and characteristic x-rays as shown in Fig. 40-13. In that figure the kinetic energy of the incident electrons is 35.0 keV. If the accelerating potential is increased to 50.0 keV, (a) what is the value of λmin, and (b) do the wavelengths of the role="math" localid="1661497027757" kαand kβlines increase, decrease, or remain the same?

Suppose that the electron had no spin and that the Pauli exclusion principle still held .Which, if any, of the present noble gases would remain in that category?

From Eq. 40-26, what is the ratio of the photon energies due to transitions in two atoms whose atomic numbers are Z and Z' ? (b) What is this ratio for uranium and aluminum? (c) For uranium and lithium?

In 1911, Ernest Rutherford modeled an atom as being a point of positive charge surrounded by a negative charge -ze uniformly distributed in a sphere of radius centered at the point. At distance within the sphere, the electric potential is V=Ze4πε0(1r-32R+r22R3).

  1. From this formula, determine the magnitude of the electric field for0≤r≤R. What are the (b) electric field and (c) potential forr≥R?

Suppose that a hydrogen atom in its ground state moves 80 cm through and perpendicular to a vertical magnetic field that has a magnetic field gradientdBdz=1.6×102T . (a) What is the magnitude of force exerted by the field gradient on the atom due to the magnetic moment of the atom’s electron, which we take to be Bohr magnetron? (b) What is the vertical displacement of the atom in the 80cm of travel if its speed is 1.2×105m/s?
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