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Question

Ionization energy of a Hydrogen like Bohr atom is 4 Rydbergs. It is given that 1 Rydberg=2.2×1018J and Bohr radius of Hydrogen atom is 53 pm, then

A
This Hydrogen like atom is of Lithium
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B
Radius of 1st orbit of this atom is 0.26 oA
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C
Wavelength of radiation emitted when electron jumps from n = 2 to n = 1 is 303 oA
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D
Radius of 1st orbit of this atom is 0.17 oA
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Solution

The correct options are
B Radius of 1st orbit of this atom is 0.26 oA
C Wavelength of radiation emitted when electron jumps from n = 2 to n = 1 is 303 oA
Ionization energy of hydrogen like atom is E=Rhc Z2 where Rhc=1 RydbergSo,4=Z2 Z=2 [Helium]
Rn=53×1012 n2Z=532×1012=26.5×1012=0.26 oA
1λ=1.1×10+7 Z2(11122)λ=1073.3=303 oA

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