Question

If an electron is moving in the ${\mathrm{n}}^{\mathrm{th}}$ orbit of the hydrogen atom, then its velocity (${\mathrm{V}}_{\mathrm{n}}$) for the ${\mathrm{n}}^{\mathrm{th}}$ orbit is given as :

• A. v_n ∝ n
• B. v_n ∝ (1/n)
• C. v_n ∝ n²
• D. v_n ∝ 1/n²

Answer 1

The correct option is B

v_n ∝ (1/n)

Explanation for the correct option:

Bohr’s Model of an Atom: According to the Bohr Atomic model, a small positively charged nucleus is surrounded by revolving negatively charged electrons in fixed orbits. He concluded that electron will have more energy if it is located away from the nucleus whereas electrons will have less energy if it located near the nucleus.

In the Bohr model of the atom, electrons travel in defined circular orbits around the nucleus. According to Bohr's atomic model:

The velocity of the electron in ${\mathrm{n}}^{\mathrm{th}}$ orbit$=\mathrm{v}=\frac{\mathrm{h}}{2{\mathrm{\pi ma}}_0}\times \frac{\mathrm{Z}}{\mathrm{n}}$

$=\mathrm{v}\propto \frac{1}{\mathrm{n}}$

Final Answer: Hence, the correct answer is option B.