Atomic Structure - Result Question 19

####19. According to Bohr’s theory,

$E _n=$ Total energy $\quad K _n=$ Kinetic energy

$V _n=$ Potential energy $\quad r^{n}=$ Radius of $n$th orbit

Match the following :

(2006, 6M)

Column I Column II
A. $V _n / K _n=$ ? p.
B. If radius of $n$th orbit $\propto E _n^{x}, x=$ ? q. $\quad-1$
Angular momentum in lowest
orbital
r. -2
D. $\frac{1}{r^{n}} \propto Z^{y}, y=?$ s.

Fill in the Blanks

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Answer:

Correct Answer: 19.

Solution:

  1. A. $V _n=-\frac{1}{4 \pi \varepsilon _0}\left(\frac{Z e^{2}}{r}\right)$

$$ \begin{aligned} K _n & =\frac{1}{8 \pi \varepsilon _0}\left(\frac{Z e^{2}}{r}\right) \ \Rightarrow \quad \frac{V _n}{K _n} & =-2-(r) \end{aligned} $$

B. $E _n=-\frac{Z e^{2}}{8 \pi \varepsilon _0 r} \propto r^{-1}$

$$ \Rightarrow \quad x=-1-(q) $$

C. Angular momentum $=\sqrt{l(l+1)} \frac{h}{2 \pi}=0$ in $1 s$-orbital D. $r _n=\frac{a _0 n^{2}}{Z} \Rightarrow \frac{1}{r _n} \propto Z-(s)$



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