Note, the values of the following fundamental constants: The Planck constant: h

Question

Note, the values of the following fundamental constants: The Planck constant: h 6.626 x 10-34 Js The charge on the electron: 1.602 19 c e x 10 The mass of the electron: m 9.111 x 10 31 kg The speed of light: c 3x 100 ms In addition: h h 2w 1. (a) What is the effective nuclear charge and why is it not the same as the atomic number? 4 marks (b) Show the arrangement of the electrons in their orbitals for the following elements i. C (Z-6), ii. Cr (Z-24). [4 marks (c) Define the ionisation energy. 2 marks (d) When ultraviolet radiation of wavelength 58.4nm from a helium lamp is directed on to a sample of krypton, electrons are injected with a speed 1.59x10 ms Calculate the ionisation energy of krypton. 4 marks (e) 25 He Ne 20 15 Kr Xe 10 Na Rb Cs 20 40 60 Atomic Number, Z Figure 1 Ionisation energy as function of atomic number Describe the trends observed in Figure 1, above, showing the ionisation energy as a function of atomic number 6 marks

Explanation / Answer

1. (a) Effective nuclear charge is the net positive charge experienced by an electron in an atom. Electrons intervening between the nucleus and an outer electron are said to shield or screen the outer electron from the nucleus so that the outer electron does not experience the full nuclear charge. The Effective nuclear charge often represented as Zeff is calculated from the atomic number and the total number of nonvalence electrons by the formula,

Zeff = Z - S

were,

Z = atomic number

S = total number of nonvalence electrons in the atom

Thus, we can see that the Zeff is different from the atomic number for an atom.

1. (b) The arrangement of electrons in the following are as below,

i. C (Z = 6) : 1s2 2s2 2p2

ii. Cr (Z = 24) : 1s2 2s2 2p6 3s2 3p6 3d5 4s1

1. (c) Ionization energy : Ionization energy is the energy required to lose an electron from an element in a gaseous state or an ion. It is the opposite of electron affinity which is the energy released when an electron is gained by an element in a gaseous phase or as an ion.

1. (d) We will use the following relation to calculate the energy of UV radiation,

E = hv = hc/lambda

were,

h = planck's constant = 6.626 x 10^-34 J.s

c = 3 x 10^8 m.s^-1

lambda = wavelength = 58.4 nm = 5.84 x 10^-8 m

substitute the values we get,

E = 6.626 x 10^-34 x 3 x 10^8 / 5.84 x 10^-8

   = 3.40 x 10^-18 J

Now, the kinetic energy of electron = 1/2 mv2

m = mass of electron taken here = 9.111 x 10^?31 kg

v = speed of an electron ejected = 1.59 x 10^-6 m.s-1

substitute the values,

kinetic energy = 1/2 (9.111 x 10^-31)(1.59 x 10^-6)

                       = 1.15 x 10^-42 J

Therefore, the ionization energy would be,

E of UV radiation - kinetic energy of electron

3.40 x 10^-18 J - 1.15 x 10^-42 J = 3.40 x 10^-18 J

therefore, the ionization energy is 3.40 x 10^-18 J

(e) The trend seen in the graph can be explained as follows. As per the definition of ionization energy explained before it is the energy required to remove an electron from a neutral atom in its gaseous phase. Ionization energy is the opposite of electronegativity. The lower this energy is the more readily the atom becomes a cation. The higher this energy is it is more unlikely that the atom becomes a cation. Generally, elements on the right side of the periodic table have a higher ionization energy because their valence shell is nearly filled. Elements on the left side of the periodic table have low ionization energies because of their willingness to lose electrons and become cations. Thus, ionization energy increases from left to right on the periodic table. It decreases slightly as we go down the group say from Li to Ca in the alkali metal series as shown in the graph. This is due to the fact that size of atoms becomes larger thereby the attraction between the valence electrons and nucleus is reduced.

Another factor that affects ionization energy is electron shielding. Electron shielding describes the ability of an atom's inner electrons to shield its positively-charged nucleus from its valence electrons. When moving to the right of a period, the number of electrons increases and the strength of shielding increases. As a result, it is easier for valence shell electrons to ionize, and thus the ionization energy decreases down a group. Electron shielding is also known as screening. The ionization energy of the elements within a period generally increases from left to right. This is due to valence shell stability. The ionization energy of the elements within a group generally decreases from top to bottom. This is due to electron shielding. The noble gases possess very high ionization energies because of their full valence shells as indicated in the graph. Note that helium has the highest ionization energy of all the elements.

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