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Estimate the difference in energy between 1st and 2nd Bohr’s orbit for a Hatom. At whatminimum atomic number (Z), a transition from n = 2 to n = 1 energy level would result in the emission ofradiation with wavelength  = 3.0  108 m ? Which Hydrogen atom like species this atomic number corre￾sponds to ? How much ionisation potential is needed to ionise this species ? (R = 1.097  107 m1)

Estimate the difference in energy between 1st and 2nd Bohr’s orbit for a Hatom. At whatminimum atomic number (Z), a transition from n = 2 to n = 1 energy level would result in the emission ofradiation with wavelength  = 3.0  108 m ? Which Hydrogen atom like species this atomic number corre￾sponds to ? How much ionisation potential is needed to ionise this species ? (R = 1.097  107 m1)

Grade:12th pass

1 Answers

Arun
25750 Points
5 years ago
∆E = RhcZ2 (1/n12 – 1/n22)
Here, R = 1.0967 * 107 m-1
h = 6.626 * 10-34 J sec, c = 3 * 108 m/sec
n1 = 1, n2 = 2 and for H-atom, Z = 1
E2 – E1 = 1.0967 * 107 * 6.626 * 10-34 * 3 * 108 (1/1 – 1/4)
∆E = 1.0967 * 6.626 * 3 * ¾ * 10-19 J
= 16.3512 * 10-19 J
= 16.3512 *10-19/1.6 *10-19 eV = 10.22 eV
∆E = hc/λ = RhcZ2 (1/n12 -1/n22)
1/λ = RZ2 (1/1 – 1/4) = RZ2 * 3/4
Given, λ = 3 * 10-8= m
∴ 1/3 *10-8 = 1.0967 = Z2 * 3/4 * 107
∴ Z2 = 108 *4/3 *3 *1.0967 *107 = 40/9 *1.0967 = 4
∴ Z = 2
So it corresponds to He+ which has 1 electron like hydrogen.

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