The electric potential between a proton and an electron is r given by V = V0 in(r/r0), where r0 is a constant. Assuming Bohr's model to be applicable, write variation of rn with n, n being the principal quantum number.

Question

The electric potential between a proton and an electron is r given by V = V0 in(r/r0), where r0 is a constant. Assuming Bohr's model to be applicable, write variation of rn with n, n being the principal quantum number. (A) rn propto n (B) rn propto (1/n) (C) rn propto n2 (D) rn propto (1/n2)

Tardigrade Admin · Accepted Answer

U=eV=eV0 in((r/r0)) |F|=|-(dU/dr)|=(eV0/r) This force will provide the necessary centripetal force. Hence, (mv2/r)=(eV0/r) or v=√(eV0/m)...(i) Moreover, mvr=(nh/2π)...(ii) Dividing Eq. (ii) by (i), we have or rn propto n

Q. The electric potential between a proton and an electron is r given by $V = V_{0} in \frac{r}{r _{0}}$ , where $r_{0}$ is a constant. Assuming Bohr's model to be applicable, write variation of rn with n, n being the principal quantum number.

$r_{n} \propto n$

$r_{n} \propto \frac{1}{n}$

$r_{n} \propto n^{2}$

$r_{n} \propto \frac{1}{n ^{2}}$

Q. The electric potential between a proton and an electron is r given by V=V0​inr0​r​, where r0​ is a constant. Assuming Bohr's model to be applicable, write variation of rn with n, n being the principal quantum number.

rn​∝n

rn​∝n1​

rn​∝n2

rn​∝n21​

U=eV=eV0​in(r0​r​) ∣F∣=∣∣​−drdU​∣∣​=reV0​​ This force will provide the necessary centripetal force. Hence, rmv2​=reV0​​ or v=meV0​​​...(i) Moreover, mvr=2πnh​...(ii) Dividing Eq. (ii) by (i), we have or rn​∝n

Q. The electric potential between a proton and an electron is r given by $V = V_{0} in \frac{r}{r _{0}}$ , where $r_{0}$ is a constant. Assuming Bohr's model to be applicable, write variation of rn with n, n being the principal quantum number.

$r_{n} \propto n$

$r_{n} \propto \frac{1}{n}$

$r_{n} \propto n^{2}$

$r_{n} \propto \frac{1}{n ^{2}}$