Correct Answer - Option 1 : Potential energy increases and kinetic energy decreases
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 potential energy of the electron in the nth orbit is given as,
\(\Rightarrow U_n=-\frac{kZe^2}{r_n}\)
\(\Rightarrow U_n\propto-\frac{1}{r_n}\) -----(1)
- And the kinetic energy is given as,
\(\Rightarrow K_n=\frac{kZe^2}{2r_n}\)
\(\Rightarrow K_n\propto\frac{1}{r_n}\) -----(2)
Where Z = atomic number, e = charge on the electron, and rn = radius of the nth orbit
- By equation 1 the potential energy is inversely proportional to the negative of the radius of the orbit, so as the radius of the orbit increases the potential energy also increases.
- By equation 2 the kinetic energy is inversely proportional to the radius of the orbit, so as the radius of the orbit increases the potential energy decreases.
- When an electron is raised from the ground state to an excited state in the hydrogen atom the radius of the orbit increases, so the potential energy increases and the kinetic energy decreases. Hence, option 1 is correct.
