ChemistryNEET 2024Bohr model and hydrogen spectrum

Structure of Atom

The energy of an electron in the ground state ( $n = 1$ ) of the $\mathrm{He^+}$ ion is $-x$ J. Then that of an electron in the $n = 2$ state of the $\mathrm{Be^{3+}}$ ion, in J, is:

A. $-\dfrac{x}{9}$
B. $-4x$
C. $-\dfrac{4x}{9}$
D. $-x$ ✓

Solution

$E_n = -\frac{Z^2}{n^2} \times 13.6$ eV. For $\mathrm{He^+}$ ( $Z=2$ , $n=1$ ): factor $4$ . For $\mathrm{Be^{3+}}$ ( $Z=4$ , $n=2$ ): factor $\frac{16}{4} = 4$ . Same factor, so the energy is $-x$ J.

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Structure of Atom

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