Correct Answer - Option 3 : Minimum energy
CONCEPT:
Bohr's Atomic Model:
- Bohr proposed a model for hydrogen atom which is also applicable for some lighter atoms in which a single electron revolves around a stationary nucleus of positive charge Ze (called hydrogen-like atom).
Bohr's model is based on the following postulates:
- He postulated that an electron in an atom can move around the nucleus in certain circular stable orbits without emitting radiations.
- Bohr found that the magnitude of the electron's angular momentum is quantized i.e.
\(\Rightarrow L = m{v_n}\;{r_n} = n\left( {\frac{h}{{2\pi }}} \right)\)
Where n = 1, 2, 3, ..... each value of n corresponds to a permitted value of the orbit radius, rn = Radius of nth orbit, vn = corresponding speed, and h = Planck's constant
EXPLANATION:
- According to Bohr's atomic model, the total energy of the electron in the nth orbit is given as,
\(\Rightarrow E_n=-13.6\frac{Z^2}{n^2}\) -----(1)
Where Z = atomic number
For the hydrogen atom (Z =1),
\(\Rightarrow E_n=-13.6\frac{1^2}{n^2}\)
\(\Rightarrow E_n=-\frac{13.6}{n^2}\)
\(\Rightarrow E_n\propto-\frac{1}{n^2}\) -----(2)
- By equation 2 it is clear that the energy of the electron is inversely proportional to the negative of the square of the number of the orbit, so in the lowest orbit, the energy of the electron will be minimum and it increases as the electron gets excited.
- Hence, option 3 is correct.
