Question

If $r$ and $v$ represent, respectively, the orbital radius and orbital velocity of the electron in the Bohr's theory of hydrogen atom, then they are proportional to the orbit number as

• A. $r\propto n,\; v\propto n$
• B. $r\propto n,\; v\propto \dfrac{1}{n^2}$
• C. $r\propto n^2,\; v\propto \dfrac{1}{n}$
• D. $r\propto \dfrac{1}{n},\; v\propto n$
• E. $r\propto n^2,\; v\propto n$

Hint:

Physics Tip: In Bohr atom, outer orbit = larger radius but slower electron.

Answer 1

The Correct Option is C

Concept:
In Bohr model of hydrogen atom: - Radius of $n^{th}$ orbit: $$r_n=n^2a_0$$ - Speed of electron in $n^{th}$ orbit: $$v_n=\frac{v_1}{n}$$ where $a_0$ is Bohr radius.
Step 1: Relation for orbital radius.
$$r\propto n^2$$ So radius increases as square of orbit number.
Step 2: Relation for orbital speed.
$$v\propto \frac{1}{n}$$ So speed decreases for higher orbit.
Step 3: Match option.
Correct relation: $$r\propto n^2,\qquad v\propto \frac{1}{n}$$ Hence correct option is (C). :contentReference[oaicite:1]{index=1}