Question

Which of the following statements are incorrect according to Bohr's theory of the hydrogen atom?

• A. Kinetic energy of the electron is maximum in the first orbit
• B. Potential energy of the electron is maximum in the first orbit
• C. Radius of the second orbit is four times the radius of the first orbit
• D. Since energy is quantised, all energy levels have equal spacing between them

Answer 1

Answer: (B), (D)

Since energy is quantised, all energy levels have equal spacing between them

$E_{total}=-\frac{13.6Z^2}{n^2}eV$
$=K.E.+P.E.=(\frac{1}{2}m{v}^2-m{v}^2)=(\frac{13.6Z^2}{n^2}-\frac{27.2Z^2}{n^2})$
a) $K.E.$ is maximum when $n=1$ (most +ve)

b) $P.E.$ is minimum when $n=1$ (most -ve) and maximum when $n=\infty$

c) We know, $r\propto \frac{n^2}{Z}$
$\frac{r_2}{r_1}=\frac{2^2}{1^2}=4$
Therefore, $r_2=4r_1$

d) $E\propto \frac{1}{n^2}$
Although energy is quantised, but the spacing between enrgy levels becomes smaller when $n$ increases.