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 the variation of $r_{n}$ ,
n being the principal quantum number

Question

Infinity Learn · Accepted Answer

Potential energy $$U=eV=eV0ln$$⁡$$rr0$$  Force $$F=$$−$$dUdr=eV0rr0$$ . Therefore the force will provide the necessary centripetal force. Hence, $$mv2r=eV0rr0$$ ⇒$$v=eV0mr0$$………(i)and$$ $$mvr=nh2$$π………$$(ii) From equations (i) and (ii),  $$meV0mr0$$⋅$$r=nh2$$π  ⇒ $$r=nh2$$$$π$$$$r0meV0$$   ⇒ rn∝n

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 the variation of $r_{n}$ ,
n being the principal quantum number

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The electric potential between a proton and an electron is given by V=V0ln⁡rr0, where r0 is a constant. Assuming Bohr's model to be applicable, write the variation of rn,n being the principal quantum number

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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 the variation of $r_{n}$ ,
n being the principal quantum number