Question

Consider the following parameters with regard to hydrogen-like atoms:
(1) Energy of the atom
(2) Radius of electron orbit
(3) Spin of the electron
Which of the above are same for all hydrogen-like atoms and ions in $n=1$ state?

• A. $1$ only
• B. $2$ only
• C. $3$ only
• D. $1$ and $2$

Answer 1

The correct option is D $1$ and $2$

For hydrogen-like atoms, the parameters (1) and (2) are the same for all hydrogen-like atoms and ions in n $=$ 1 state.

(1) Energy of the atom. In the first orbit of the atom, the energy is same for different atoms/ions.

(2) Radius of electron orbit. For the first orbit of the atom, the radius is same for different atoms/ions.

(3) Spin of the electron can be either $+\frac{1}{2}$ or $-\frac{1}{2}$. Thus, the spin is different.