Question

According to Bohr’s theory, the electronic energy of $H$-atom in Bohr’s orbit is given by

• A. $E_{n}=-\frac{2.18 \times 10^{-19} \times Z}{2n^{2}}\,J$
• B. $E_{n}=-\frac{2.179 \times 10^{-18} \times Z^{2}}{n^{2}}\,J$
• C. $E_{n}=-\frac{21.79 \times 10^{-18} \times Z}{2n^{2}}\,J$
• D. $E_{n}=-\frac{21.8 \times 10^{-21} \times Z^{2}}{n^{2}}\,J$

Answer 1

Answer: (B)

According to Bohr's theory, the energy of electron in $n ^{\text {th }}$ Bohr's orbit of $H$-atom or hydrogen-like atoms/ions is given by:
$E _{ n }=- R _{ H } \frac{ Z ^{2}}{ n ^{2}}$
where $R _{ H }=2.18 \times 10^{-18} J$
and $Z =$ atomic number, $n = n ^{\text {th }}$ orbit
Thus, $E _{ n }=-2.18 \times 10^{-18} \times \frac{ Z ^{2}}{ n ^{2}} J$