Question

Electron volt is the unit of energy$(1\,eV=1.6\times {{10}^{-19}}J)$. In H-atom, the binding energy of an electron in the first orbit is 13.6 eV. The same in joule (J) is?
$A.\,10\times {{10}^{-19}}J$
$B.\,21.76\times {{10}^{-19}}J$
$C.\,13.6\times {{10}^{-19}}J$
D. None of these

Answer 1

This is a direct question, basically a unit conversion question is given. The conversion formula is given in the question statement itself, so, we will make use of the same to solve this problem.
Complete step by step so

Complete step-by-step solution
The abbreviation of the electron volt is eV. The abbreviation of the Joule is J. Firstly, we need to check whether the unit conversion is possible or not.
The electron volt is the unit of energy. The joule is the unit of energy. As the units of the energy are electron volt and the joule. So, unit conversion is possible. Now, we can continue with the problem.
From the given question statement, the unit conversion formula is available, so, we will make use of the same to carry out the calculation.
The unit conversion formula is,
$1\,eV=1.6\times {{10}^{-19}}J$
As the binding energy of an electron in the first orbit is 13.6 eV, so, we need to multiply this value on both sides of the above equation. So, we get,

& 13.6\times 1\,eV=13.6\times 1.6\times {{10}^{-19}}J \\\ & 13.6eV=21.76\times {{10}^{-19}}J \\\ \end{aligned}$$ $$\therefore $$ The binding energy of electron in first orbit in terms of the unit Joule is $$\,21.76\times {{10}^{-19}}J$$ **As, the binding energy of the electron in first orbit in terms of the unit Joule is equal to the value of$$\,21.76\times {{10}^{-19}}J$$, thus, option (B) is correct.** **Note:** The units of the parameters should be known to solve the problem. As, in this question, they have provided the conversion formula, so we have made use of the same, otherwise, we are supposed to remember these unit conversion formulae. Sometimes, to check the knowledge of students, the non-related units of the parameters will be given.