Question

In a hypothetical $H$-atom the mass of an electron is $7$ times the original and the charge is double of what we consider, then calculate the energy of electron on the $1^{st}$ orbit of such a hypothetical $H$-atom?

• A. $-13.6\times {10}^{3}eV$
• B. $-1.52\times {10}^{3}eV$
• C. $-15.2\times {10}^{3}eV$
• D. $-1.36\times {10}^{3}eV$

Answer 1

Answer: (B)

$-1.52\times {10}^{3}eV$

The expression for the energy of the electron is $E_n=-\frac{2{\pi }^2{Z}^2{e}^{4}m{K}^2}{n^2{h}^2}$
The energy of an electron in the first orbit of the hydrogen atom is -13.6eV.
When in a hypothetical H-atom, the mass of an electron is 7 times the original and the charge is double of what we consider then the energy of electron on the 1st orbit of such a hypothetical H-atom will be proportional to $m{e}^4$.
It will be equal to $-13.6\times 7\times 2^4=-13.6\times 112eV=-1.52\times {10}^{3}eV$.