Atoms And Nuclei Question 303
Question: In a hypothetical system, a particle of mass m and charge -3q is moving around a very heavy particle charge q. Assume that Bohr’s model is applicable to this system, then velocity of mass m in the first orbit is
Options:
A) $ \frac{3q^{2}}{2{\varepsilon_{0}}h} $
B) $ \frac{3q^{2}}{4{\varepsilon_{0}}h} $
C) $ \frac{3q}{2\pi {\varepsilon_{0}}h} $
D) $ \frac{3q}{4\pi {\varepsilon_{0}}h} $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \frac{mv^{2}}{r}=\frac{3q^{2}}{4\pi {\varepsilon_{0}}r^{2}}\Rightarrow mvr=\frac{3q^{2}}{4\pi {\varepsilon_{0}}v} $ ..(i)
and $ \frac{nh}{2\pi }=mvr $ .(ii)
Using (i) and (ii) and putting n=1
$ \frac{h}{2\pi }=\frac{3q^{2}}{4\pi {\varepsilon_{0}}v}\Rightarrow v=\frac{3q^{2}}{2{\varepsilon_{0}}h} $
