Question

The acceleration of electron in the first orbit of a hydrogen atom is (where the symbols have their usual meanings)

• A. $\frac{4 \pi ^{2} m}{h^{3}}$
• B. $\frac{h^{2}}{4 \pi ^{2} m r}$
• C. $\frac{h^{2}}{4 \pi ^{2} m^{2} r^{3}}$
• D. $\frac{m^{2} h^{2}}{4 \pi ^{2} r^{3} \, }$

Answer 1

Answer: (C)

From $mvr=\frac{n h}{2 \pi },v=\frac{n h}{2 \pi m r}$
For the first Bohr orbit, $n=1$
Acceleration, $a=\frac{v^{2}}{r}=\frac{n^{2} h^{2}}{4 \left(\pi \right)^{2} m^{2} r^{2} \left(\right. r \left.\right)}=\frac{h^{2}}{4 \left(\pi \right)^{2} m^{2} r^{3}}$