Question 321: Atoms & Nuclei

Question

Suppose an electron is attracted towards the origin by a force $${k \over r}$$ where $$'k'$$ is a constant and $$'r'$$ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the $${n^{th}}$$ orbital of the electron is found to be $$'{r_n}'$$ and the kinetic energy of the electron to be $$'{T_n}'.$$ 
Then which of the following is true?

Accepted Answer

When $$F = {k \over r} = $$ centripetal force, then $${k \over r} = {{m{v^2}} \over r}$$
$$ \Rightarrow m{v^2} = $$ constant $$ \Rightarrow $$ kinetic energy is constant
$$ \Rightarrow T$$ is independent of $$n.$$

Answer

$${T_n} \propto {1 \over {{n^2}}},{r_n} \propto {n^2}$$

Answer

$${T_n}$$ independent of $$n,{r_n} \propto n$$

Answer

$${T_n} \propto {1 \over n},{r_n} \propto n$$

Answer

$${T_n} \propto {1 \over n},{r_n} \propto {n^2}$$

Atoms & Nuclei

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