Question

Energy of an electron in the second orbit of hydrogen atom is E and the energy of electron in 3rd orbit of He will be:

• A. $E_3=\frac{16E}{3}$
• B. $E_3=\frac{16E}{9}$
• C. $E_3=\frac{4E}{9}$
• D. $E_3=\frac{4E}{3}$

Answer 1

Answer: (B)

The energy for nth orbit in the atom of atomic number (Z) is given by $E_n=\frac{Z^2}{n^2}{E}_0$ So, for helium (Z = 2) and n = 3 $\therefore$ for third orbit $E_3=\frac{4}{9}{E}_0$ ?(1) Now for H atom (Z = 1) and n = 2 $\therefore$ for second orbit $E_2=\frac{1}{4}{E}_0$ ?(2) Now from Eqs. (1) and (2), we obtain $\frac{E_3}{E_2}=\frac{\frac{4}{9}{\epsilon }_0}{\frac{1}{4}{E}_0}=\frac{16}{9}$ or $E_3=\frac{16}{9}{E}_2=\frac{16}{9}E$