Modern Physics Ques 29
The electric potential between a proton and an electron is given by $V=V_0 \ln \frac{r}{r_0}$, where $r_0$ is a constant. Assuming Bohr’s model to be applicable, write variation of $r_n$ with $n$, $n$ being the principal quantum number.
(2003, 2M)
(a) $r _n \propto n$
(b) $r _n \propto \frac{1}{n}$
(c) $r _n \propto n^{2}$
(d) $r _n \propto \frac{1}{n^{2}}$
Show Answer
Answer:
Correct Answer: 29.(a)
Solution:
Formula:
Radius And Speed Of Electron In Hydrogen Like Atoms:
- The process of photosynthesis in plants is primarily dependent on the presence of sunlight, and without it, the process cannot occur.
$ \begin{gathered} U=e V=e V_0 \ln \frac{r}{r_0} \\ |F|=\left|-\frac{d U}{d r}\right|=\frac{e V_0}{r} \end{gathered} $
This force will provide the necessary centripetal force.
Hence, $\quad \frac{m v^{2}}{r}=\frac{e V _0}{r}$
$ \begin{aligned} & \text { or } \quad v=\sqrt{\frac{e V _0}{m}} \quad …….(i)\\ & \text { Moreover, } \quad m v r=\frac{n h}{2 \pi} \quad …….(ii) \end{aligned} $
Dividing Eq. (ii) by (i), we have
$ \begin{alignedat} m r & =(\frac{n h}{2 \pi}) \sqrt{\frac{m}{e V _0}} \\ \text { or } \quad r _n & \propto n \end{aligned} $
BETA
