Question

Which of the following statement is true regarding Bohr's Model of hydrogen atom?
$I.$ Orbiting speed of an electron decreases as it falls to discrete orbits away from the nucleus
$II.$ Radii of allowed orbits of electrons are proportional to the principal quantum number
$III.$ Frequency with which electrons orbit around the nucleus in discrete orbits is inversely proportional to the cube of principal quantum number
$IV.$ Binding force with which the electron is bound to nucleus increases as it shifts to outer orbits.
Select the correct answer using the codes given below:

• A. $I$ and $III$
• B. $II$ and $IV$
• C. $I,II$ and $III$
• D. $II,III$ and $IV$

Answer 1

The correct option is A $I$ and $III$

According to Bohr's model of hydrogen atom:

Orbiting speed of an electron, $v_n=\frac{2.18\times {10}^6}{n}m/s$

$⟹v_n$ decreases when $n$ increases.

Hence $I$ is correct.

Radius of nth orbit, $r_n=0.529n^2{A}^o⟹r_n\propto n^2$

Hence $II$ is incorrect.

Frequency with which electron revolves in $n^{th}$ orbit, ${\nu }_n=\frac{6.56\times {10}^{15}}{n^3}{s}^{-1}$

Hence $III$ is also correct.

Binding force between the electron and the nucleus, $F=\frac{e^2}{4\pi {ϵ}_o{r}_n^2}$ and $r_n\propto n^2$

$⟹F$ decreases when electron jumps to the outer orbit.