(a) Explanation Given data: The states of Helium ion are n = 1, 2, 3 . Formula used: The radius of the He + ion is given by: r n = h 2 4 π 2 Z k C e 2 m e n 2 Here, n = 1, 2, 3, . . . represents the state of the atom, m e is the mass of the electron, e is the magnitude of the charge on the electron, h is the Planck’s constant, Z is the atomic number of the atom and k C is the Coulomb's constant. The expression for the energy of the He + ion for different states is given by the Bohr model as follows: E n = ( − 13.6 eV ) Z 2 n 2 Here, n = 1, 2, 3, . . . represents the states of the atom and Z is the atomic number of the atom. Explanation: Recall the expression for the radius of the He + ion. r n = h 2 4 π 2 Z k C e 2 m e n 2 Substitute, 6.63 × 10 − 34 J ⋅ s for h , 9.00 × 10 9 N ⋅ m 2 ⋅ C − 2 for k C , 1 .6 × 10 − 19 C for e , 2 for Z and 9 .11 × 10 − 31 kg for m e . r n = ( 6.63 × 10 − 34 J ⋅ s ) 2 4 π 2 ( 2 ⋅ ( 9.00 × 10 9 N ⋅ m 2 ⋅ C − 2 ) ) ⋅ ( 1 .6 × 10 − 19 C ) 2 ⋅ (9 .11 × 10 − 31 kg) n 2 = 1 2 ( 0.53 × 10 − 10 m ) n 2 ……(1) Substitute, 1 for n in equation (1). r 1 = 1 2 ( 0.53 × 10 − 10 m ) ⋅ ( 1 ) 2 = ( 0.27 × 10 − 10 m ) ⋅ ( 10 9 nm 1 m ) = 0 (b) To determine The energy state diagram for He + ion.

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Chapter 28, Problem 59GP

(a)

To determine

The radii and energies of the n= 1, 2 and 3 states of the He+ (Helium) ion.

(b)

To determine

The energy state diagram for He+ ion.

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Chapter 28, Problem 58P

Chapter 28, Problem 60GP

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The radii and energies of the n = 1, 2 and 3 states of the He + (Helium) ion.

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The radii and energies of the n= 1, 2 and 3 states of the He+ (Helium) ion.

The energy state diagram for He+ ion.

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Chapter 28 Solutions