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Modern Physics> In mathematical representation of bohr's ...

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In mathematical representation of bohr's energy,
En = KE + PE
En = 1/2 mv2 + (– KZe2 / rn)
here, can you please explain me how can we arrive at the above mentioned value of potential energy??

Sashank Sharma , 8 Years ago

Grade 11

1 Answers

Eshan

Dear student,

This is the potential energy of system of an electron and nucleus of the atom with sepraration of $r_n$ between them. Charge of the electron is $e$ and that of nucleus of atomic number $Z$ is $Ze$ .

Hence the force acting on the electron at distance $r$ is $-\dfrac{k(Ze)(e)}{r^2}$ .
Hence the work done in bring charge from infinity to its orbit = Potential energy of the sytsem= $-\int_\infty^{r_n}(-\dfrac{kZe^2}{r^2})dr$
$=-\dfrac{kZe^2}{r_n}$

Last Activity: 7 Years ago

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