Question

Ionization energy of a Hydrogen like Bohr atom is $4Rydbergs$. It is given that $1Rydberg=2.2\times {10}^{-18}J$ and Bohr radius of Hydrogen atom is 53 pm, then

• A. This Hydrogen like atom is of Lithium
• B. Radius of 1st orbit of this atom is 0.26 $\stackrel{o}{A}$
• C. Wavelength of radiation emitted when electron jumps from n = 2 to n = 1 is 303 $\stackrel{o}{A}$
• D. Radius of 1st orbit of this atom is 0.17 $\stackrel{o}{A}$

Answer 1

Answer: (B), (C)

The correct options are
B Radius of 1st orbit of this atom is 0.26 $\stackrel{o}{A}$
C Wavelength of radiation emitted when electron jumps from n = 2 to n = 1 is 303 $\stackrel{o}{A}$

Ionization energy of hydrogen like atom is $E=Rhc{Z}^2$ where $Rhc=1RydbergSo,4=Z^2\Rightarrow Z=2$ [Helium]
$R_n=53\times {10}^{-12}\frac{n^2}{Z}=\frac{53}{2}\times {10}^{-12}=26.5\times {10}^{-12}=0.26\stackrel{o}{A}$
$\frac{1}{\lambda }=1.1\times {10}^{+7}{Z}^2(\frac{1}{1}-\frac{1}{2^2})\Rightarrow \lambda =\frac{{10}^{-7}}{3.3}=303\stackrel{o}{A}$